Researcher Database

Yuzuru Sato
Research Institute for Electronic Science Research Center of Mathematics for Social Creativity
Associate Professor

Researcher Profile and Settings

Affiliation

  • Research Institute for Electronic Science Research Center of Mathematics for Social Creativity

Job Title

  • Associate Professor

URL

Research funding number

  • 30342794

J-Global ID

Research Interests

  • Nonlinear phenomena   Dynamical systems   Chaos   Fluctuation and noise   Spatio-temporal chaos   Complex systems   Non-autonomous dynamical systems   Stochastic bifurcation   Noise-induced phenomena   Stochastic chaos   Random dynamical systems   

Research Areas

  • Natural sciences / Applied mathematics and statistics
  • Natural sciences / Basic mathematics
  • Informatics / Sensitivity (kansei) informatics
  • Informatics / Soft computing
  • Natural sciences / Mathematical physics and basic theory
  • Informatics / Computational science

Academic & Professional Experience

  • 2013/09 - Today London Mathematical Laboratory External Fellow
  • 2006 - Today Hokkaido University RIES/Department of Mathematics Associate professor
  • 2002 - 2006 Santa Fe Institute Postdoctoral Fellow
  • 2001 - 2002 RIKEN Special Postdoctoral Researcher
  • 2000 - 2001 University of Tokyo / JSPS Postdoctoral researcher

Education

  • 1997/04 - 2000/03  University of Tokyo  Graduate School of Arts and Sciences

Association Memberships

  • Society for Industrial and Applied Mathematics   American Physical Society   日本応用数理学会   日本物理学会   

Research Activities

Published Papers

  • Faranda Davide, Sato Yuzuru, Messori Gabriele, Moloney Nicholas R, Yiou Pascal
    EARTH SYSTEM DYNAMICS 10 (3) 555 - 567 2190-4979 2019/09/19 [Refereed][Not invited]
  • Yuzuru Sato, Rainer Klages
    Physical Review Letters 122 (17) 174101  0031-9007 2019/04/29 [Refereed][Not invited]
  • Moloney Nicholas R, Faranda Davide, Sato Yuzuru
    CHAOS 29 (2) 022101  1054-1500 2019/02 [Refereed][Not invited]
  • Kunihiko Esashi, Tamotsu Onozaki, Yoshitaka Saiki, Yuzuru Sato
    Structural Change and Economic Dynamics 44 68 - 76 0954-349X 2018/03/01 [Refereed][Not invited]
     
    Empirical studies often conclude that multi-regional business cycles exhibit intermittent transition between synchronization and desynchronization of each regional fluctuations. In this study, we robustly observe this behavior (called chaotic itinerancy) in a model of multi-regional business cycles, in which all regions of a national economy are homogeneous and connected through producers’ behavior based on the average level announced by the government. Although a producer very slowly adjusts his/her output towards the average level, regional business cycles begin to synchronize because of the entrainment effect. Moreover, when a producer emphasizes the profit maximization more and when puts more weight on the average level in his/her decision-making, the economy is more likely to exhibit such intermittent transition. Further, it is clarified that behind intermittent transition exist cycles among periodic orbits with different number of unstable directions.
  • D. Faranda, Y. Sato, B. Saint-Michel, C. Wiertel, V. Padilla, B. Dubrulle, F. Daviaud
    PHYSICAL REVIEW LETTERS 119 (1) 014502  0031-9007 2017/07 [Refereed][Not invited]
     
    We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely, the number of quasistationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can be recovered neither using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low-dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasistationary states.
  • Anna Maria Cherubini, Jeroen S. W. Lamb, Martin Rasmussen, Yuzuru Sato
    NONLINEARITY 30 (7) 2835 - 2853 0951-7715 2017/07 [Refereed][Not invited]
     
    We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a nonautonomous forcing. We prove the existence of a unique global attracting random periodic orbit and a stationary periodic measure. We use the stationary periodic measure to define an indicator for the stochastic resonance.
  • Stochastic chaos in random dynamical systems
    Yuzuru Sato
    RIMS Technical Report (No.2028) pp.1-8  2017 [Not refereed][Not invited]
  • Davide Faranda, Giacomo Masato, Nicholas Moloney, Yuzuru Sato, Francois Daviaud, Berengere Dubrulle, Pascal Yiou
    CLIMATE DYNAMICS 47 (5-6) 1587 - 1599 0930-7575 2016/09 [Refereed][Not invited]
     
    Atmospheric mid-latitude circulation is dominated by a zonal, westerly flow. Such a flow is generally symmetric, but it can be occasionally broken up by blocking anticyclones. The subsequent asymmetric flow can persist for several days. In this paper, we apply new mathematical tools based on the computation of an extremal index in order to reexamine the dynamical mechanisms responsible for the transitions between zonal and blocked flows. We discard the claim that mid-latitude circulation features two distinct stable equilibria or chaotic regimes, in favor of a simpler mechanism that is well understood in dynamical systems theory: we identify the blocked flow as an unstable fixed point (or saddle point) of a single basin chaotic attractor, dominated by the westerlies regime. We also analyze the North Atlantic Oscillation and the Arctic Oscillation atmospheric indices, whose behavior is often associated with the transition between the two circulation regimes, and investigate analogies and differences with the bidimensional blocking indices. We find that the Arctic Oscillation index, which can be thought as a proxy for a hemispheric average of the Tibaldi-Molteni blocking index, tracks unstable fixed points. On the other hand, the North Atlantic Oscillation, representative only for local properties of the North Atlantic blocking dynamics, does not show any trace of the presence of unstable fixed points of the dynamics.
  • Sato Yuzuru, Ay Nihat
    IEICE NONLINEAR THEORY AND ITS APPLICATIONS 7 (2) 118 - 125 2185-4106 2016 [Refereed][Not invited]
  • Sato Yuzuru, Shimaoka Daisuke, Fujimoto Koichi, Taga Gentaro
    IEICE NONLINEAR THEORY AND ITS APPLICATIONS 7 (2) 226 - 233 2185-4106 2016 [Refereed][Not invited]
  • Robust pattern construction in two-dimensional neural field
    Yuzuru Sato
    Proc. of AFCA pp.85-89  2015 [Refereed][Not invited]
  • The switching between zonal and blocked mid-latitude atmospheric circulation: a dynamical system perspective
    Davide Faranda, Giacomo Masato, Nicholas Moloney, Yuzuru Sato, Francois Daviaud, Berengere Dubrulle, Pascal Yiou
    Climate Dynamics pp 1-13  2015 [Refereed][Not invited]
  • ランダム力学系と確率カオス
    佐藤譲
    数理科学 2015年8月号 26 - 31 2015 [Not refereed][Not invited]
  • Random basin in dice roll
    Y. Sato, N. Matsunaga
    RIMS Technical Report 1942 1 - 10 2015 [Not refereed][Not invited]
  • Kota Hiratsuka, Yuzuru Sato, Zin Arai
    NOLTA 5 (4) 410 - 423 2014 [Refereed][Not invited]
  • Random dynamical systems modeling for brain wave synchrony
    Kazuhiro Matsumoto, Yuzuru Sato, Hiroshi Endo, Keiichi Kitajo
    Proc. of NOLTA 2013 395 - 398 2013 [Refereed][Not invited]
  • Robust computation in two dimensional neural field
    Yuzuru Sato, Shun-ichi Amari
    Advances in Cognitive Neurodynamics 123 - 129 2013 [Refereed][Not invited]
  • Computability and Complexity of Julia Sets
    Kota Hiratsuka, Yuzuru Sato, Zin Arai
    Proc. of NOLTA 2013 2 - 5 2013 [Refereed][Not invited]
  • Random dynamics from time series
    Yuzuru Sato
    RIMS Technical Report 1827 24 - 32 2012 [Not refereed][Not invited]
  • Random dynamics from time-serieses of physiological rhythms.
    Yuzuru Sato, Kazuhiro Matsumoto
    Proc. of NOLTA 2012 497 - 500 2012 [Refereed][Not invited]
  • Miguel Angel Fuentes, Yuzuru Sato, Constantino Tsallis
    PHYSICS LETTERS A 375 (33) 2988 - 2991 0375-9601 2011/08 [Refereed][Not invited]
     
    We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initial conditions, entropy production, and escape rate, in z-logistic maps for both positive and zero Lyapunov exponents. We unify these relations at chaos, where the Lyapunov exponent is positive, and at its onset, where it vanishes. Our result unifies, in particular, two already known cases, namely (i) the standard entropy rate in the presence of escape, valid for exponential functionality rates with strong chaos, and (ii) the Pesin-like identity with no escape, valid for the power-law behavior present at points such as the Feigenbaum one. (C) 2011 Elsevier B.V. All rights reserved.
  • Yao Lu, Yuzuru Sato, Shun-ichi Amari
    NEURAL COMPUTATION 23 (5) 1248 - 1260 0899-7667 2011/05 [Refereed][Not invited]
     
    A neural field is a continuous version of a neural network model accounting for dynamical pattern forming from populational firing activities in neural tissues. These patterns include standing bumps, moving bumps, traveling waves, target waves, breathers, and spiral waves, many of them observed in various brain areas. They can be categorized into two types: a wave-like activity spreading over the field and a particle-like localized activity. We show through numerical experiments that localized traveling excitation patterns (traveling bumps), which behave like particles, exist in a two-dimensional neural field with excitation and inhibition mechanisms. The traveling bumps do not require any geometric restriction (boundary) to prevent them from propagating away, a fact that might shed light on how neurons in the brain are functionally organized. Collisions of traveling bumps exhibit rich phenomena; they might reveal the manner of information processing in the cortex and be useful in various applications. The trajectories of traveling bumps can be controlled by external inputs.
  • Random dynamics from time-seriese of rotating fluid
    Yuzuru Sato, Makoto Iima, Yuji Tasaka
    Hokkaido University Technical Report 979 2011 [Not refereed][Not invited]
  • Makoto Iima, Yu Iijima, Yuzuru Sato, Yuji Tasaka
    Theor. Appl. Mech. Jpn. 59 187 - 193 2011 [Refereed][Not invited]
  • 佐藤譲
    数理解析研究所講究録 京都大学 1688 137 - 143 2010/05 [Not refereed][Not invited]
  • 回転流体自由界面の不規則スイッチングにおける底面-側壁ギャップの影響
    田坂 裕司, 飯間 信, 佐藤 讓
    日本流体力学会年会2010拡張要旨集 2010 [Not refereed][Not invited]
  • オートマトンモデルの背景
    佐藤譲
    現代思想「現代数学の思考法」 2010年9月号 155 - 163 2010 [Not refereed][Not invited]
  • 佐藤 讓, 飯間 信, 田坂 裕司
    第59回理論応用力学講演会講演論文集 145 - 146 2010 [Not refereed][Not invited]
  • 飯間 信, 飯島 悠宇, 佐藤 讓, 田坂 裕司
    第59回理論応用力学講演会講演論文集 143 - 144 2010 [Not refereed][Not invited]
  • 佐藤譲
    電子情報通信学会技術研究報告. NLP, 非線形問題 社団法人電子情報通信学会 109 (269) 221 - 223 0913-5685 2009/11 [Not refereed][Not invited]
     
    一次元単峰写像の雑音誘起現象を、加法性雑音存在下でのロジスティック写像とBelousov-Zhabotinsky写像(BZ写像)の振る舞いを数値的に調べて得た結果を例に取り考察する。(1)雑音誘起カオス(Noise-induced Chaos)と雑音誘起秩序(Noise-induced Order)が外部雑音の揺らぎの大きさに応じて共存する。(2)これらの現象は窓領域でロバストに観察される。潜在的カオス系とその観測可能性、雑音誘起現象へのランダム力学系アプローチを議論する。
  • 自由表面大変形を伴う円筒容器内の回転流れの実験および数理的解析
    飯間 信, 田坂 裕司, 佐藤 讓, 眞山 博幸
    日本流体力学会年会2008講演論文集 2008 [Not refereed][Not invited]
  • ルールを生成する力学系: 関数マップ概説
    佐藤譲
    統計数理研究所共同研究リポート 217 33 - 44 2008 [Not refereed][Not invited]
  • Random Dynamics from Time Seriese of Rotating Fluid
    Yuzuru Sato, Makoto Iima, Yuji Tasaka
    Proceedings of JSIAM 08 317 - 318 2008 [Not refereed][Not invited]
  • Yuzuru Sato, Constantino Tsallis
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 16 (6) 1727 - 1738 0218-1274 2006/06 [Refereed][Not invited]
     
    Many natural and artificial systems whose range of interaction is long enough are known to exhibit (quasi) stationary states that defy the standard, Boltzmann-Gibbs statistical mechanical prescriptions. For handling such anomalous systems (or at least some classes of them), nonextensive statistical mechanics has been proposed based on the entropy S-q = k (1 - Sigma(w)(i-1) p(i)(q))/(q - 1), with S-1 = -k Sigma(w)(i=1) p(i)lnp(i) (Boltzmann-Gibbs entropy). Special collective correlations can be mathematically constructed such that the strictly additive entropy is now S-q for an adequate value of q not equal 1, whereas Boltzmann-Gibbs entropy is nonadditive. Since important classes of systems exist for which the strict additivity of Boltzmann-Gibbs entropy is replaced by asymptotic additivity (i.e. extensivity), a variety of classes are expected to exist for which the strict additivity of S-q (q not equal 1) is similarly replaced by asymptotic additivity (i.e. extensivity). All probabilistically well defined systems whose adequate entropy is S-1 are called extensive (or normal). They correspond to a number W-eff of effectively occupied states which grows exponentially with the number N of elements (or subsystems). Those whose adequate entropy is S-q (q not equal 1) are currently called nonextensive (or anomalous). They correspond to W-eff growing like a power of N. To illustrate this scenario, recently addressed [Tsallis, 2004] we provide in this paper details about systems composed by N = 2, 3 two-state subsystems.
  • Y Sato, E Akiyama, JP Crutchfield
    PHYSICA D-NONLINEAR PHENOMENA 210 (1-2) 21 - 57 0167-2789 2005/10 [Refereed][Not invited]
     
    We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by the dynamics of uncertainty, giving a novel view of collective adaptation. (c) 2005 Elsevier B.V. All rights reserved.
  • C Tsallis, M Gell-Mann, Y Sato
    PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 102 (43) 15377 - 15382 0027-8424 2005/10 [Refereed][Not invited]
     
    Phase space can be constructed for N equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy S(BG) equivalent to -k Sigma(i) p(i) In p(i) to be extensive, i.e., S(BG)(N) proportional to N for N -> infinity. In particular, if they are independent, S(BG) is strictly additive, i.e., S(BG)(N) = NS(BG)(1), for all N. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy S(q) equivalent to k[l - Sigma(i) p(i)(q)]/(q - 1) (with S(1) = S(BG)) for some special value of q not equal 1 to be the one which is extensive [i.e., Sq(N) proportional to N for N -> infinity]. Another concept which is relevant is strict or asymptotic scale-freedom (or scale-in variance), defined as the situation for which all marginal probabilities of the N-system coincide or asymptotically approach (for N -> infinity) the joint probabilities of the (N - 1)-system. If each subsystem is a binary one, scale-freedom is guaranteed by what we hereafter refer to as the Leibnitz rule, i.e., the sum of two successive joint probabilities of the N-system coincides or asymptotically approaches the corresponding joint probability of the (N - 1)-system. The kinds of interplay of these various concepts are illustrated in several examples. One of them justifies the title of this paper. We conjecture that these mechanisms are deeply related to the very frequent emergence, in natural and artificial complex systems, of scale-free structures and to their connections with nonextensive statistical mechanics. Summarizing, we have shown that, for asymptotically scale-invariant systems, it is S(q) with q not equal 1, and not S(BG), the entropy which matches standard, clausius-like, prescriptions of classical thermodynamics.
  • Extensivity and entropy production
    Constantino Tsallis, Murray Gell-Mann, Yuzuru Sato
    Europhysics News 36 (6) 186 - 189 2005 [Refereed][Not invited]
  • Y Sato, T Ikegami
    MINDS AND MACHINES 14 (2) 133 - 143 0924-6495 2004/05 [Refereed][Not invited]
     
    This paper considers undecidability in the imitation game, the so-called Turing Test. In the Turing Test, a human, a machine, and an interrogator are the players of the game. In our model of the Turing Test, the machine and the interrogator are formalized as Turing machines, allowing us to derive several impossibility results concerning the capabilities of the interrogator. The key issue is that the validity of the Turing test is not attributed to the capability of human or machine, but rather to the capability of the interrogator. In particular, it is shown that no Turing machine can be a perfect interrogator. We also discuss meta-imitation game and imitation game with analog interfaces where both the imitator and the interrogator are mimicked by continuous dynamical systems.
  • 多体学習のダイナミクス
    佐藤譲
    2000年4月号 76 - 82 2004 [Not refereed][Not invited]
  • Y Sato, JP Crutchfield
    PHYSICAL REVIEW E 67 (1) 015206  1539-3755 2003/01 [Refereed][Not invited]
     
    Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through environment-mediated interactions. An application to rock-scissors-paper game interactions shows that the collective learning dynamics exhibits a diversity of competitive and cooperative behaviors. These include quasiperiodicity, stable limit cycles, intermittency, and deterministic chaos-behaviors that should be expected in heterogeneous multiagent systems described by the general replicator equations we derive.
  • Weaverのコミュニケーションの問題と情報理論
    佐藤譲
    統計数理研究所共同研究リポート 171 55 - 57 2003 [Not refereed][Not invited]
  • Y Sato, E Akiyama, JD Farmer
    PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 99 (7) 4748 - 4751 0027-8424 2002/04 [Refereed][Not invited]
     
    We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy.
  • 学習のダイナミクス
    佐藤譲
    統計数理研究所共同研究リポート 163 77 - 87 2002 [Not refereed][Not invited]
  • Y Sato, M Taiji, T Ikegami
    UNCONVENTIONAL MODELS OF COMPUTATION UMC' 2K, PROCEEDINGS 234 - 247 2001 [Refereed][Not invited]
     
    A dynamical systems based model of computation is studied, and we demonstrate the computational ability of nonlinear mappings. There exists a switching map system with two types of baker's map to emulate any Turing machine. The baker's maps correspond to the elementary operations of computing such as left/right shift and reading/writing of symbols in Turing machines. Taking other mappings with second-order nonlinearity (e.g. the Henon map) as elementary operations, the switching map system becomes an effective analog computer executing parallel computation similarly to MRAM. Our results show that, with bitwise Boolean AND, it has PSPACE computational power. Without bitwise Boolean AND, it is expected that its computational power is between classes RP and PSPACE. These dynamical systems execute more unstable computation than that of classical Turing machines, and this suggests a trade-off principle between stability of computation and computational power.
  • 計算のダイナミクス
    佐藤譲
    統計数理研究所共同研究リポート 144 1 - 8 2001 [Not refereed][Not invited]
  • R Ohira, Y Sato, JD Cowan
    ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 12 12 314 - 320 1049-5258 2000 [Refereed][Not invited]
     
    We study here a simple stochastic single neuron model with delayed self-feedback capable of generating spike trains. Simulations show that its spike trains exhibit resonant behavior between "noise" and "delay". In order to gain insight into this resonance, we simplify the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this simplified model we can analytically compute interspike interval histograms, and show how the resonance between noise and delay arises. The resonance is also observed when such elements are coupled through delayed interaction.
  • Yuzuru Sato, Takashi Ikegami
    J. UCS 6 (9) 881 - 905 2000 [Refereed][Not invited]
  • Computation with switching map systems
    Yuzuru Sato, Takashi Ikegami
    Journal of Universal Computer Sciences Vol. 6 (No. 9) 881-894  2000 [Refereed][Not invited]
  • Y Sato, M Taiji, T Ikegami
    COMPUTER PHYSICS COMMUNICATIONS 121 51 - 53 0010-4655 1999/09 [Refereed][Not invited]
     
    The geometrical structure of a formal language class is studied in relation with its time-complexity. A typical NP-complete problem, kSAT, is discussed by visualizing its problem space and a strict connection is made between the self-similarity and the time-complexity of the languages by constructing adequate iterated function systems (IFSs), There exist IFS classes which generate whole satisfiable Boolean expressions embedded on a unit hyper-cube, Our numerical results for the Hausdorff dimension of kSAT suggest the difference of IFS classes for 2 and 3SAT. (C) 1999 Elsevier Science B.V. All rights reserved.
  • Toru Ohira, Yuzuru Sato
    Physical Review Letters 82 (14) 2811 - 2815 1079-7114 1999 [Refereed][Not invited]
     
    We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of “noise” and “delay.” We demonstrate numerically and analytically that we can observe resonant phenomena between the oscillatory behavior due to noise and that due to delay. © 1999 The American Physical Society.
  • Undecidability of the Imitation Game
    Yuzuru Sato, Takashi Ikegami
    Proceedings of Symposium on Imitation in Animals and Artifacts 157 - 159 1999 [Refereed][Not invited]
  • Self-similar sets as satisfiable Boolean expressions
    Y Sato, M Taiji, T Ikegami
    UNCONVENTIONAL MODELS OF COMPUTATION 352 - 370 1998 [Refereed][Not invited]
     
    Recursive operations are common procedures in the fields of computational theory and fractal geometry. Recently, computational theory has paid much attention to fractal geometry. In this paper, the geometrical structure of a formal language class is studied in relation with its time-complexity. A typical NP-complete problem, kSAT, is discussed by visualizing its problem space. A strict connection is made between the self-similarity and the time-complexity of the languages by constructing adequate iterated function systems (IFSs). There exist IFS classes which generate whole satisfiable Boolean expressions embedded on a unit hyper-cube. The difference in time-complexity between 2SAT and 3SAT is connected to IFS classes which generate satisfiable Boolean expressions. That is, the class P complexity is related to what we call monotone IFS and the class NP or upper complexity does to more complex IFS. Our numerical results for the Hausdorff dimension of satisfiable Boolean expressions suggest the difference of IFS classes between 2 and 3SAT.

Books etc

Conference Activities & Talks

  • Stochastic bifurcation and intermittency in random dynamical systems  [Invited]
    Yuzuru Sato
    RIMS workshop  2019/10
  • Anomalous diffusion in random dynamical systems  [Invited]
    Yuzuru Sato
    The Mathematics of Climate and Environment, IHP  2019/10
  • Anomalous diffusion and intermittency in deterministic /random dynamical systems  [Not invited]
    Yuzuru Sato
    RIMS workshop  2019/09
  • Stochastic bifurcation in a turbulent swirling flow  [Not invited]
    Yuzuru Sato
    JSIAM  2019/09
  • Anomalous diffusion and intermittency in random dynamical systems  [Not invited]
    Yuzuru Sato
    Seminar at Tokyo Metropolitan University,  2019/09
  • Noise-induced Statistical Periodicity in Lasota-Mackey Maps  [Not invited]
    Yuzuru Sato
    RIMS workshop  2019/08
  • Anomalous diffusion in random dynamical systems  [Invited]
    Yuzuru Sato
    DCP19  2019/07
  • Stochastic bifurcation in a turbulent swirling flow  [Invited]
    Yuzuru Sato
    ICIAM  2019/07
  • Stochastic bifurcation in a turbulent swirling flow  [Not invited]
    Yuzuru Sato
    RIMS workshop  2019/06
  • Stochastic bifurcation in a turbulent swirling flow  [Not invited]
    Yuzuru Sato
    Workshop on data analysis and machinelearning in dynamical systems  2019/05
  • Stochastic bifurcation in a turbulent swirling flow  [Invited]
    Yuzuru Sato
    CRITICS workshop, Imperial College London  2019/03
  • Stochastic chaos in random dynamical systems and its application to time series analysis  [Invited]
    Yuzuru Sato
    Seminar at University of Pisa  2018/10
  • Stochastic bifurcation in random dynamical systems and its application to modeling atmospheric jet dynamics  [Invited]
    Yuzuru Sato
    “Dynamical Systems and Climate Dynamics,” LSCE/CNRS-Saclay  2018/10
  • Stochastic bifurcation in random logistic map  [Not invited]
    Yuzuru Sato
    Dynamics Days Europe  2018/09
  • Stochastic chaos in a turbulent swirling flow  [Invited]
    Yuzuru Sato
    LML summer school, London Mathematical Laboratory  2018/08
  • Stochastic chaos in a turbulent swirling flow  [Not invited]
    Yuzuru Sato
    MIMS seminar  2018/07
  • Stochastic chaos in a turbulent swirling flow  [Invited]
    Yuzuru Sato
    CIMPA spring school, Vietnam Academy of Science and Technology  2018/03
  • Stochastic chaos in a turbulent swirling flow  [Invited]
    Yuzuru Sato
    Lorentz Center Workshop on Random Dynamical Systems  2017/12
  • Anomalous diffusion and intermittency in random dynamical systems  [Invited]
    Yuzuru Sato
    Statistical and nonlinear physics seminar at CNRS  2017/11
  • Stochastic bifurcation and early warning signals in random logistic maps  [Not invited]
    Yuzuru Sato
    Predicting extremes in climate dynamics  2017/10
  • Anomalous diffusion and intermittency in random dynamical systems  [Not invited]
    Yuzuru Sato
    workshop on nonlinearity and complexity  2017/09
  • Anomalous diffusion and intermittency in random dynamical systems  [Invited]
    Yuzuru Sato
    ANOCOS, Tempare, Finland  2017/08
  • Anomalous diffusion and intermittency in random dynamical systems  [Not invited]
    Yuzuru Sato
    seminar at Tokyo Metroplitan University  2017/06
  • Stochastic chaos in a turbulent swirling flow  [Not invited]
    Yuzuru Sato
    RIMS workshop  2017/06
  • Crutchfield-Shaw information theory for noisy chaos: a review  [Not invited]
    Yuzuru Sato
    RIMS workshop  2017/06
  • Stochastic bifurcation in random logistic maps  [Invited]
    Yuzuru Sato
    SIAM Conference on Applications of Dynamical systems  2017/05
  • Anomalous diffusion and intermittency in random dynamical systems  [Invited]
    Yuzuru Sato
    Kyoto Dynamics Days: Random Dynamical Systems Theory and Its Applications, Kyoto University  2017/04
  • Noise-induced bifurcations in a random logistic map  [Invited]
    Yuzuru Sato
    Kyoto Dynamics Days: Random Dynamical Systems Theory and Its Applications, Kyoto University  2017/04
  • Anomalous diffusion and intermittency in random dynamical systems  [Not invited]
    Yuzuru Sato
    JSIAM  2017/03
  • Stochastic bifurcation in random logistic maps  [Not invited]
    Yuzuru Sato
    Keno Dynamics Days  2017/01
  • Stochastic bifurcation in random logistic maps  [Invited]
    Yuzuru Sato
    Applications of statical-mechanics and dynamical systems to climate, LSCE, CEA, CNRS  2016/11
  • Anomalous diffusion in random dynamical systems,  [Invited]
    Yuzuru Sato
    Dynamics Days Latin America and the Caribbean, University of Puebla  2016/10
  • Anomalous diffusion in random dynamical systems,  [Invited]
    Yuzuru Sato
    Hokkaido-Pisa Summer Institute, University of Pisa  2016/09
  • Anomalous diffusion in random dynamical systems,  [Invited]
    Yuzuru Sato
    Workshop on Anomalous Dynamics and Weak ergodicity breaking, University of Warwick  2016/08
  • Chaos in function dynamics  [Invited]
    Yuzuru Sato
    RIMS workshop  2016/07
  • Noise-induced statistical periodicity and almost cyclic sets  [Not invited]
    Yuzuru Sato
    RIMS workshop  2016/06
  • Anomalous diffusion in random dynamical systems  [Not invited]
    Yuzuru Sato
    Workshop on dynamical systems and computation  2016/03
  • Neural Field dynamics for growing brains  [Invited]
    Yuzuru Sato
    AAAS panel presentation, AAAS  2016/02
  • Robust computation in neural field  [Invited]
    Yuzuru Sato
    AFCA keynote talk, CANDAR  2015/12
  • Robust pattern construction in neural field  [Not invited]
    Yuzuru Sato
    seminar at Kyoto University  2015/11
  • Chaos in random and non-autonomous dynamical systems  [Invited]
    Yuzuru Sato
    Complex systems summer school  2015/07
  • Dynamics of Neural Field  [Invited]
    Yuzuru Sato
    Seminar at University of Tokyo  2015/03
  • Random strange attractors and stochastic chaos  [Invited]
    Yuzuru Sato
    Workshop on dynamical systems and computation  2015/03
  • Random Strange Attractors and Stochastic Chaos  [Not invited]
    Yuzuru Sato
    Dynamical Systems and Computation, Sapporo  2015/02
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    Seminar at University of Sussex Brighton UK  2014/11
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    Max Planck Institute, Dynamics and Self-organization  2014/10
  • Random basin in dice roll  [Invited]
    Yuzuru Sato
    Workshop on Theory and Applications of Random/Nonautonomous Dynamical Systems  2014/09
  • Asymmetric game dynamics and its applications  [Invited]
    Yuzuru Sato
    SAET  2014/08
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    Workshop on Computation and Computability in Dynamics, Trieste  2014/07
  • Random dynamics from time seiries of rotating fluids  [Not invited]
    Yuzuru Sato
    Workshop on Physical Origins of Correlated Extreme Events  2014/06
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    Seminar at Loughborough University Loughborough  2014/05
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    Mini Conference on Glassy and Complex Systems  2014/05
  • Random dynamical systems approaches to noise-induced phenomena  [Not invited]
    Yuzuru Sato
    Open Statistical Physics  2014/03
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    Dynamical Systems, Fluid Dynamics and Lagrangian Coherent Structures  2014/03
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    ランダム力学系理論とその応用 京都府京都市  2014/02
  • Random basin in dice roll  [Invited]
    Yuzuru Sato
    ランダム力学系理論とその応用  2014/02
  • Stability and diversity in collective adaptation  [Invited]
    Yuzuru Sato
    Seminar at Manchester University  2014/02
  • Real number computation and dynamical systems  [Invited]
    Yuzuru Sato
    Dynamical systems and computation  2014/01
  • Random dynamics from time series  [Invited]
    Yuzuru Sato
    SIAM Conference on Applications of Dynamical systems  2013/05
  • Noise-induced phenomena in one-dimensional maps  [Invited]
    Yuzuru Sato
    Seminar at Hitotsubashi University  2013/04
  • Asymmetric game dynamics and its applications  [Invited]
    Yuzuru Sato
    Seminar at King’s College London  2013/04
  • Randomness in noised dynamical systems  [Invited]
    Yuzuru Sato
    Ergodic theory, information theory and computer sciences  2013/04
  • Partial Control of Chaos and Continuity of Safe Sets  [Not invited]
    G. Wang, Y. Sato
    Dynamics Days US  2013/01
  • Randomness of Perturbed Dice Throw Dynamics  [Not invited]
    N. Matsunaga, Y. Sato
    Dynamics Days US  2013/01
  • Random Dynamics from a Time Series of Physiological Rhythms  [Invited]
    Yuzuru Sato
    NOLTA2012  2012/10
  • Asymmetric game dynamics and its applications  [Invited]
    Yuzuru Sato
    CICS Colloquium, Universidad del Desarrollo  2012/10
  • Random dynamical systems approaches to noise-induced phenomena  [Invited]
    Yuzuru Sato
    Summer Workshop on Artificial Minds and Real Brains  2012/08
  • Noise-induced phenomena and their applications  [Invited]
    Yuzuru Sato
    Workshop on Open dynamical systems: Ergodic Theory, Probabilistic Methods and Applications, BIRS Banff Canada  2012/04
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Seminar at Soongsil University Seoul, Korea  2012/04
  • Noise-induced phenomena and their applications: interaction between deterministic chaos and stochastic randomness  [Invited]
    Yuzuru Sato
    Nonlinear Science Colloquium at Waseda University  2012/04
  • Noise-induced phenomena and their applications: interaction between deterministic chaos and stochastic randomness  [Invited]
    Yuzuru Sato
    International workshop on Anomalous Statistics, Generalized Entropies, and Information Geometry  2012/03
  • Random dynamics from time-series and its applications  [Invited]
    Yuzuru Sato
    NOLTA2011  2011/09
  • Noise-induced phenomena in one-dimensional maps  [Not invited]
    Yuzuru Sato
    Weak Chaos, Infinite Ergodic Theory, and Anomalous Dynamics  2011/08
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Kyoto interdisciplinary Dynamics Seminar  2011/07
  • Robust Computation in Two-dimensional Neural Field  [Invited]
    Yuzuru Sato
    The 3rd International Conference on Cognitive Neurodynamics  2011/06
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    SIAM Conference on Applications of Dynamical systems  2011/05
  • Asymmetric game dynamics and its extensions  [Invited]
    Yuzuru Sato
    Game theory workshop, Nagoya  2011/05
  • Random nonlinear phenomena and its applications  [Invited]
    Yuzuru Sato
    Yakushima Workshop  2011/04
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Seminar at Department of Applied Mathematics at the University of Colorado at Boulder  2011/04
  • Asymmetric game dynamics and its extensions  [Not invited]
    Yuzuru Sato
    Game theory workshop  2011/03
  • Noise-induced statistical periodicity and its applications  [Invited]
    Yuzuru Sato
    Dynamics of Complex Systems  2011/03
  • 回転流体系における自由表面の不規則スイッチング現象の決定論性の推定  [Not invited]
    飯島 悠宇, 田坂 裕司, 佐藤 讓, 飯間 信
    2010年度応用数学合同研究集会  2010/12
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    NIMS Hot Topics Workshop on Applied Dynamical Systems  2010/12
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Max-Planck Institute, Mathematics in the Sciences  2010/12
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Kagoshima workshop on nonlinear and Nonequilibrium dynamics  2010/10
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    RIKEN Mathematical Science Workshop  2010/09
  • Robust computation in activation-inhibition field  [Invited]
    Yuzuru Sato
    The 9th international conference on unconventional computation  2010/06
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Niseko workshop on mathematical biology  2010/04
  • Noise-induced phenomena in one dimensional maps  [Not invited]
    Yuzuru Sato
    日本物理学会  2010/03
  • Noise-induced phenomena in one dimensional maps: hidden fragility in nonlinear dynamics  [Invited]
    Yuzuru Sato
    Sapporo winter school on nonlinear science  2010/02
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    NIMS Hot Topics, Workshop on Applied Dynamical Systems “Dynamics in Network and Mathematical Neuroscience,” NIMS  2010/02
  • Stability and diversity in collective adaptation  [Invited]
    Yuzuru Sato
    Chaos revolution in Science  2009/12
  • Statistics and dynamical analysis of surface switching in rotating fluid  [Not invited]
    Y. Tasaka, M. Iima, Y. Sato
    16th International Couette-Taylor Workshop Princeton  2009/09
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Dynamics of Complex Systems  2009/08
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Biology and Control, SICE  2009/05
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Behavior and Logic of Cellular Systems, RIKEN  2009/04
  • High-dimensional chaotic dynamics in an N-person game  [Invited]
    Yuzuru Sato
    Seminar at Kyushu University  2009/04
  • Noise-induced phenomena in one dimensional maps  [Invited]
    Yuzuru Sato
    Workshop: Fluctuation and Noise in Living Organisms, RIKEN  2009/04
  • Chaos in function dynamics  [Invited]
    Yuzuru Sato
    Seminar at GCOE workshop, Kobe University  2009/04
  • Random Dynamics from Time Serieses of Rotating Fluid  [Not invited]
    Yuzuru Sato
    応用数理学会  2008/09
  • Random Dynamics from Time Serieses of Rotating Fluid  [Invited]
    Yuzuru Sato
    ynamics Days Asia-Pacific  2008/09
  • Random Dynamics from Time Serieses of Rotating Fluid  [Invited]
    Yuzuru Sato
    Dynamics of Complex systems  2008/09
  • Limit of Analog Computation  [Invited]
    Yuzuru Sato
    Seminar at University of Tokyo  2008/04
  • Re-visiting Noise-induced Order  [Not invited]
    Yuzuru Sato
    Artificial Life: Half-way through  2008/04
  • Noise-induced Phenomena in one-dimensional maps  [Not invited]
    Yuzuru Sato
    Seminar at ASI, RIKEN  2008/04
  • Function Dynamics: An Introductory Review  [Not invited]
    Yuzuru Sato
    動的システムの情報論VII  2007/11
  • Heteroclinic Cycles in N-person Game Dynamics  [Invited]
    Yuzuru Sato
    inisymposium at SIAM Conference on Application of Dynamical Systems Snowbird, Utah USA  2007/05
  • N-person Game Dynamics  [Invited]
    Yuzuru Sato
    Seminar at Santa Fe Institute  2007/04
  • Stability and Diversity in Collective Adaptation  [Not invited]
    Yuzuru Sato
    Seminar at Department of Physical Chemistry Fritz Haber Institute  2006/04
  • Stability and Diversity in Collective Adaptation  [Invited]
    Yuzuru Sato
    Long-term workshop at Isaac Newton Institute, Cambridge, England, UK  2005/09
  • patiotemporal Intermittency and its Application to Problems of Memory and Learning  [Invited]
    Yuzuru Sato
    Seminar at JAIST  2005
  • Dynamics of learning in Rock-Scissors-Paper game  [Invited]
    Yuzuru Sato
    Seminar at KNU Daegu, Korea  2005
  • Spatiotemporal Intermittency and its Application to Problems of Memory and Learning  [Invited]
    Yuzuru Sato
    Seminar at Santa Fe Institute, Santa Fe, New Mexico, USA  2005
  • Stability and Diversity in Collective Adaptation  [Invited]
    Yuzuru Sato
    Seminar at Santa Fe Institute, Santa Fe, New Mexico, USA  2004
  • Dynamics of Learning and Flows of Information in Collectives  [Invited]
    Yuzuru Sato
    Dynamics Days Europe XXIII, Palma de Mallorca, Spain  2003/09
  • Dynamics of Analog Computation  [Invited]
    Yuzuru Sato
    Philosophy of Computation  2003
  • Dynamics of coupled replicator equations  [Not invited]
    Yuzuru Sato
    "Dynamics Days Europe XXII", Heiderberg, Germany  2002/07
  • Dynamics of learning and coupled replicator  [Invited]
    Yuzuru Sato
    Workshop on Dynamical Systems in Mathematical Biology, Tokyo, Japan  2002/05
  • Coupled replicator equations for the dynamics of learning in multiagent systems  [Invited]
    Yuzuru Sato
    Seminar at Research Unit in Language Evolution and Computation, University of Edinburgh  2002
  • Computation with switching map systems: Nonlinearity and computational complexity  [Invited]
    Yuzuru Sato
    Seminar at Department of Applied Mathematics, Princeton University Princeton, NJ, USA  2001
  • NP-completeness of kSAT and multifractals  [Not invited]
    Yuzuru Sato
    Conference on Computational Physics, Granada, Spain  1998/09

MISC

  • 佐藤譲  日本応用数理学会年会講演予稿集(CD-ROM)  2019-  487  2019/08/21  [Not refereed][Not invited]
  • Yuzuru Sato, Kathrin Padberg-Gehle  2019/05/08  [Not refereed][Not invited]
     
    Noise-induced statistical periodicity in a class of one-dimensional maps is
    studied. We show the existence of statistical periodicity in a modified
    Lasota-Mackey map and describe the phenomenon in terms of almost cyclic sets. A
    transition from a stable state to a periodic state of the density depending on
    the noise level is observed in numerical investigations based on trajectory
    averages and by means of a transfer operator approach. We conclude that the
    statistical periodicity is the origin of the almost periodicity in
    noise-induced order.
  • Yuzuru Sato, Thai Son Doan, Jeroen S, W. Lamb, Martin Rasmussen  2018/11/10  [Not refereed][Not invited]
     
    The emergence of noise-induced chaos in a random logistic map with bounded
    noise is understood as a two-step process consisting of a topological
    bifurcation flagged by a zero-crossing point of the supremum of the dichotomy
    spectrum and a subsequent dynamical bifurcation to a random strange attractor
    flagged by a zero crossing point of the Lyapunov exponent. The associated three
    consecutive dynamical phases are characterized as a random periodic attractor,
    a random point attractor, and a random strange attractor, respectively. The
    first phase has a negative dichotomy spectrum reflecting uniform attraction to
    the random periodic attractor. The second phase no longer has a negative
    dichotomy spectrum - and the random point attractor is not uniformly attractive
    - but it retains a negative Lyapunov exponent reflecting the aggregate
    asymptotic contractive behaviour. For practical purposes, the extrema of the
    dichotomy spectrum equal that of the support of the spectrum of the finite-time
    Lyapunov exponents. We present detailed numerical results from various
    dynamical viewpoints, illustrating the dynamical characterisation of the three
    different phases.
  • Yuzuru Sato, Nihat Ay  819-  2006/11  [Not refereed][Not invited]
     
    Dynamics of information flow in adaptively interacting stochastic processes
    is studied. We give an extended form of game dynamics for Markovian processes
    and study its behavior to observe information flow through the system. Examples
    of the adaptive dynamics for two stochastic processes interacting through
    matching pennies game interaction are exhibited along with underlying causal
    structure.

Awards & Honors

  • 2013/09 London Mathematical Laboratory LML External Fellowship
     
    受賞者: Yuzuru Sato
  • 1998/06 Santa Fe Institute Complex Systems Summer School Fellowship
     
    受賞者: Yuzuru Sato

Research Grants & Projects

  • ランダムな実および複素力学系、正則写像半群とフラクタル幾何学の研究
    文部科学省:科学研究費補助金(基盤研究(B))
    Date (from‐to) : 2019 -2023 
    Author : 角 大輝
  • 確率過程論的アプローチによるランダム力学系の理論研究
    文部科学省:挑戦的研究(萌芽)
    Date (from‐to) : 2019 -2021 
    Author : 矢野孝次
  • 古典および量子統計的システムにおける新規な情報幾何構造の探究
    文部科学省:科学研究費補助金(基盤研究(B))
    Date (from‐to) : 2017 -2021 
    Author : 藤原彰夫
  • ランダム力学系理論に基づく確率カオスの現象論とその応用
    文部科学省:科学研究費補助金(基盤研究(C))
    Date (from‐to) : 2018 -2020 
    Author : 佐藤譲
  • ヒト脳の形態形成から行動生成に至る発達のダイナミクス
    文部科学省:科学研究費補助金(基盤研究(S))
    Date (from‐to) : 2014 -2019 
    Author : 多賀 厳太郎
  • 文部科学省:科学研究費補助金(基盤研究(C))
    Date (from‐to) : 2014 -2018 
    Author : 佐藤 譲
  • 低次元の確率分岐の研究
    文部科学省:特別研究員奨励費
    Date (from‐to) : 2015 -2017 
    Author : 佐藤譲
  • 文部科学省:科学研究費補助金(基盤研究(C))
    Date (from‐to) : 2012 -2014 
    Author : 佐藤 譲, 角 大輝, 矢野 孝次
     
    ノイズと決定論的力学の相互作用に伴う雑音誘起現象は非線形物理学では古くから研究されてきた問題です。例えば確率共鳴、ノイズ同期、雑音誘起カオスがその典型例です。近年ノイズ強度に応じて多重転移を示す現象(多重雑音誘起現象)、ノイズ強度に依存して軌道分布が多様な振動を起こす現象(統計的周期性)といった、これまでに知られていなかった雑音誘起現象が、広いクラスの非線形系に偏在していることがわかってきました。本研究の目的は「雑音誘起現象論」の体系化を進めるとともに、ランダム力学系において、「決定論カオス」に相当する複雑現象を概念化し、数理科学的に基礎づけることにあります。(A) 様々な雑音誘起現象のメカニズムとその普遍性、現象クラスの分析研究代表者の先行研究によると、多段回の雑音誘起転移を示す多重雑音誘起現象、軌道密度が振動する統計的周期性は興奮系で普遍的であることが数値的に検証されました。さらに雑音誘起ベイシンを数値的に見いだし、その普遍性を理論的に解析中です。(B) 大自由度多スケール系の実験時系列解析大自由度多スケール系の実験データとして(3)ヒトの脳波(提供者:北城圭一、理化学研究所)についてランダム結合振動子系によるモデリングを行いました。また新たに(4)ダイスロールのダイナミクス(提供者: Tomasz Kapitaniak、Lodz Technical University)のランダム力学系モデルによる時系列解析をすすめました。この結果は松永伸夫氏の修士論文としてまとめられ、現在出版準備中です。
  • 文部科学省:科学研究費補助金(基盤研究(C))
    Date (from‐to) : 2012 -2014 
    Author : 角 大輝, 佐藤 譲
     
    ランダム複素力学系と有理関数の半群(以下有理半群という)の力学系を研究した。ランダム複素多項式力学系においては、大概のシステムにおいて、(通常の意味では)カオス性がなくなること(協調原理)の論文を雑誌に発表した。また、このような乱雑性誘起現象(通常の力学系では起こらない、ランダム力学系特有の現象)の研究を行った。乱雑性誘起現象(または雑音誘起現象)は物理サイドで非常に活発に研究されており、それらについて北海道大学の佐藤譲氏と何度も議論を重ねた。ランダムな複素力学系と有理半群の同時発展を目指した基礎理論に基づき、2(または3)元生成で臨界値集合が有界な多項式半群の空間を詳しく調べ、以前の結果をさらに精密化し一般化した。特に、高木関数の複素平面上版をも含めた様々な複素平面上の特異な関数の、ジュリア集合上での微分不可能性などの、ランダム化によるカオス消滅後に残る複雑さを詳しく解析した。J. Jaerisch氏と共同研究を行って、それらの関数の各点ヘルダー指数に関するマルチフラクタル解析を行って論文にまとめ、学術雑誌に投稿した。また、Jaerisch氏と、無限生成双曲的有理半群の力学系を研究し、それを応用して、有限生成で双曲的とは限らない有理半群の力学系を研究して論文にまとめ、学術雑誌に投稿した。さらに、R. Stankewitz氏を大阪大学に招き共同研究を行い、有理半群のジュリア集合を描くプログラムの数学的妥当性を支える定理を示し、論文にまとめ学術雑誌に投稿した。M. Urbanski氏との共同研究において、開集合条件を満たすとは限らない双曲的有限生成有理半群のジュリア集合のハウスドルフ次元を調べ、横断性条件という緩やかでかつチェック可能な条件のもとで、Bowenの公式がほとんどすべてのパラメータで成り立つことを論文にまとめて学術雑誌に出版し、さらに研究を発展させた。
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2009 -2011 
    Author : Yuzuru SATO
     
    We extend the standard game dynamics to N-person game dynamics, Markov game dynamics, and continuous game dynamics and study them in terms of dynamical systems theory. (1) N-person game dynamics : The model is described as coupled map lattice and globally coupled maps, and shows complex nonlinear behavior such as traveling waves, spatiotemporal chaos, spatiotemporal intermittency. (2) Markov game dynamics : Players are modeled not by probability distributions, but by simple Markov systems. We analyze them dynamical systems theoretically and information theoretically. (3) Continuous game dynamics : Mixed strategies for continuous actions are modeled as probability density functions and a PDE model is constructed.
  • 文部科学省:科学研究費補助金(特別研究員奨励費)
    Date (from‐to) : 1999 -2000 
    Author : 佐藤 譲

Educational Activities

Teaching Experience

  • Analytic Studies
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : カオス、複雑性、ランダムネス
  • Advanced Mathematical Analysis
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : カオス、複雑性、ランダムネス
  • Linear Algebra I
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 行列, 連立1次方程式, 基本変形, 階数, 行列式, 逆行列

Social Contribution

Social Contribution

Social Contribution

  • Open campus Hokkaido University
    Date (from-to) : 2006-Today
    Role : Lecturer
    Sponser, Organizer, Publisher  : Hokkaido University
    Event, Program, Title : Open campus Hokkaido University
  • 滞在型研究所での研究活動とその成果
    Date (from-to) : 2018/07/11
    Role : Panelist
    Sponser, Organizer, Publisher  : 東北大学
    Event, Program, Title : 紐帯の織り手:ネットワーク形成の極意とアカデミアの役割
  • Neural field dynamics in growing brains
    Date (from-to) : 2016-2016
    Role : Panelist
    Sponser, Organizer, Publisher  : AAAS
    Event, Program, Title : AAAS
  • Chaos and randomness
    Date (from-to) : 2016-2016
    Role : Lecturer
    Event, Program, Title : JSPSサイエンス・ダイアログ
  • Newtonian mechanics
    Date (from-to) : 2014-2014
    Role : Lecturer
    Sponser, Organizer, Publisher  : London Mathematical Laboratory
    Event, Program, Title : Summer project for secondary school students at London Japanese School

Others

  • 2014 -2014 コンサルタント
    ZonLab, London, UK コンサルタント(2014-現在)
  • 2010 -2010 コンサルタント
    ヤマハ発動機株式会社 技術コンサルタント (2010-2013)


Copyright © MEDIA FUSION Co.,Ltd. All rights reserved.