Yuzuru Sato | Hokkaido University (original) (raw)

Papers by Yuzuru Sato

WORLD SCIENTIFIC eBooks, Feb 1, 2010

Phase space can be constructed for N equal and distinguishable subsystems that could be probabili... more 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 ϵ ؊k ͚i pi ln pi to be extensive, i.e., S BG(N) ؔ N for N 3 ؕ. In particular, if they are independent, SBG is strictly additive, i.e., S BG(N) ‫؍‬ NSBG(1), ᭙N. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy S q ϵ k[1 ؊ ͚i p i q ]͞(q ؊ 1) (with S1 ‫؍‬ SBG) for some special value of q 1 to be the one which is extensive [i.e., S q (N) ؔ N for N 3 ؕ]. Another concept which is relevant is strict or asymptotic scale-freedom (or scale-invariance), defined as the situation for which all marginal probabilities of the N-system coincide or asymptotically approach (for N 3 ؕ) 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 1, and not SBG, the entropy which matches standard, clausius-like, prescriptions of classical thermodynamics.

Zenodo (CERN European Organization for Nuclear Research), Sep 28, 2000

A dynamical systems based model of computation is studied. We demonstrate the computational capab... more A dynamical systems based model of computation is studied. We demonstrate the computational capability of a class of dynamical systems called switching map systems. There exists a switching map system with two t ypes of baker's map to emulate any T uring machines. The baker's maps are corresponding to the elementary operations of Turing machines such as left right head-moving and read write symbols. A connection between the generalized shifts by C. Moore Moore 91 and the inputoutput mappings by L. Blum et al. Blum, Cucker, Shub and Smale 98 is shown with our model. We present four concrete examples of switching map systems corresponding to the Chomsky hierarchy. T aking non-hyperbolic mappings as elementary operations, it is expected that the switching map systems shows a new model of computation with nonlinearity as an oracle.

Chaos, Oct 1, 2020

It has been shown that a permutation can uniquely identify the joint set of an initial condition ... more It has been shown that a permutation can uniquely identify the joint set of an initial condition and a non-autonomous external force realization added to the deterministic system in given time series data. We demonstrate that our results can be applied to time series forecasting as well as the estimation of common external forces. Thus, permutations provide a convenient description for a time series data set generated by non-autonomous dynamical systems.

RePEc: Research Papers in Economics, Sep 1, 2001

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attem... more We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her͞his 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 twoperson 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.

Physica D: Nonlinear Phenomena, 2021

In order to elucidate the plateau phenomena caused by vanishing gradient, we herein analyse stabi... more In order to elucidate the plateau phenomena caused by vanishing gradient, we herein analyse stability of stochastic gradient descent near degenerated subspaces in a multi-layer perceptron. In stochastic gradient descent for Fukumizu-Amari model, which is the minimal multi-layer perceptron showing non-trivial plateau phenomena, we show that (1) attracting regions exist in multiply degenerated subspaces, (2) a strong plateau phenomenon emerges as a noise-induced synchronisation, which is not observed in deterministic gradient descent, (3) an optimal fluctuation exists to minimise the escape time from the degenerated subspace. The noise-induced degeneration observed herein is expected to be found in a broad class of machine learning via neural networks.

In this paper, we discuss robust computation represented by collective motion of large neural dyn... more In this paper, we discuss robust computation represented by collective motion of large neural dynamics. There exist stable traveling bumps and their collisions in a two dimensional neural field. By using the stable traveling bumps and their collisions, arbitrary logical operations can be constructed. The resulting computation processes in the neural field is structurally and orbitally stable and the basin measure of the dynamics of the computations is finitely positive. Thus, the computations are robust and constructive in the framework of dynamical systems theory.

IEICE Proceeding Series, 2014

A random dynamical systems model is studied to understand coupled dynamics of auditory area and m... more A random dynamical systems model is studied to understand coupled dynamics of auditory area and motor area modulated by external force. We measure transfer entropy of coupled oscillators with the presence of noise to explain results of human brain wave experiments.

arXiv (Cornell University), Nov 9, 2018

The emergence of noise-induced chaos in a random logistic map with bounded noise is understood as... more 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.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022

We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a... more We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a class of one-dimensional random dynamical system with additive noise. The result is achieved with the help of rigorous computer assisted estimates. We first approximate the stationary distribution of the random dynamical system and then compute certified error intervals for the Lyapunov exponent. We find that the sign of the Lyapunov exponent changes at least three times when increasing the noise amplitude. We also show numerical evidence that the standard non-rigorous numerical approximation by finite-time Lyapunov exponent is valid with our model for a sufficiently large number of iterations. Our method is expected to work for a broad class of nonlinear stochastic phenomena.

arXiv: Dynamical Systems, 2018

In this paper, we show that under a generic condition of the coefficient of a stochastic phase os... more In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is always negative. Consequently, the generated random dynamical system exhibits a synchronization.

Theoretical and applied mechanics Japan, 2011

Earth System Dynamics Discussions, 2018

We derive a minimal dynamical model for the northern hemisphere mid-latitude jet dynamics by embe... more We derive a minimal dynamical model for the northern hemisphere mid-latitude jet dynamics by embedding atmospheric data, and investigate its properties (bifurcation structure, stability, local dimensions) for different atmospheric flow regimes. We derive our model according to the following steps: i) obtain a 1-D description of the mid-latitude jet-stream by computing the position of the jet at each longitude using the ERA-Interim reanalysis, ii) use the embedding procedure to derive a map of the local jet position dynamics, iii) introduce the coupling and stochastic effects deriving from both atmospheric turbulence and topographic disturbances to the jet. We then analyze the dynamical properties of the model in different regimes: i) one that gives the closest representation of the properties extracted from real data, ii) one featuring a stronger jet (strong coupling), iii) one featuring a weaker jet (low coupling), iv) modified topography. We argue that such a simple model provides a useful description of the dynamical properties of the atmospheric jet.

Nonlinear Theory and Its Applications, IEICE, 2016

Information flow in adaptively interacting stochastic processes is studied. We give an extended f... more Information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for interacting Markovian processes and compute a measure of causal information flow, which is different from the transfer entropy. In the game theoretic situation, causal information flow can show oscillatory behavior through reward-maximizing adaptation of two players. The adaptive dynamics for the coin-tossing game is exemplified and the causal information flow therein is investigated.

Unconventional Models of Computation, UMC’2K, 2001

Abstract. A dynamical systems based model of computation is studied, and we demonstrate the compu... more Abstract. 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 ...

Europhysics News, 2005

I t is our pleasure to welcome Jean Pierre Boon and Constantino Tsallis as guests Editors for the... more I t is our pleasure to welcome Jean Pierre Boon and Constantino Tsallis as guests Editors for the present Special Issue of Europhysics News on "Nonextensive Statistical Mechanics". They did a great job not only in selecting an impressive set of distinguished authors but also in writing the introductory Editorial and in each being a co-author of one of the contributions. The subject is difficult and could not go without a higher proportion of equations than usual in EPN: our thanks go to the EPN designer who had to face a heavier task than usual. It is sometimes necessary to address arduous developments to cover recent progress in Physics. This time, EPN will ask its readers to make an effort. It is always rewarding. The guests Editors were so efficient that the collected material passes largely the size of a standard EPN issue. We are grateful to the Publisher for accepting to accommodate all the articles in a single volume. It will make of this Special Issue the general reference work on "nonextensive statistical mechanics". Back to the usual mix of wide-ranging Features and News next time! The Editors

Physics Letters A, 2011

We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initi... more We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initial conditions, entropy production, and escape rate, in zlogistic 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.

AIP Conference Proceedings, 2000

ABSTRACT We first study here a simple stochastic dynamical equation with delayed self-feedback. T... more ABSTRACT We first study here a simple stochastic dynamical equation with delayed self-feedback. The model is investigated numerically and we find that its dynamics show an emergent regular ``spiking'' behavior, by ``tuning'' its ``noise'' and ``delay''. In order to gain insight into this ``resonance'', we abstract the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this abstracted model we can analytically capture the time interval histograms between spikes, and discover how the resonance between noise and delay arises. The resonance is also observed when such stochastic binary elements are coupled through delayed interaction. .

A random dynamics is extracted from time series of laminar-turbulent transition in rotating fluid... more A random dynamics is extracted from time series of laminar-turbulent transition in rotating fluid in an open cylinder. We focus on the dynamics of the surface height in the central region and measure switching dynamics between different quasi-stationary states and intensity of underlying turbulence. Density of return map is constructed from an one dimensional map with an stochastic term from the experimental data. It is shown that the random dynamics whose noise amplitude depends on the slow variable describes the observed macroscopic features of rotating fluid in terms of noise-induced phenomena.

IEICE Proceeding Series, 2014

A random dynamics with two stochastic terms is modeled based on a time series of physiological ex... more A random dynamics with two stochastic terms is modeled based on a time series of physiological experimental data to study synchrony between human heartbeats and pedaling rhythms modulated by music. We investigate reproduced time series, rotation numbers, and invariant densities in the model to explain transitory stagnation motion of synchrony in the experiments.

Starting with a group of reinforcement-learning agents we derive coupled replicator equations tha... more 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.

WORLD SCIENTIFIC eBooks, Feb 1, 2010

Phase space can be constructed for N equal and distinguishable subsystems that could be probabili... more 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 ϵ ؊k ͚i pi ln pi to be extensive, i.e., S BG(N) ؔ N for N 3 ؕ. In particular, if they are independent, SBG is strictly additive, i.e., S BG(N) ‫؍‬ NSBG(1), ᭙N. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy S q ϵ k[1 ؊ ͚i p i q ]͞(q ؊ 1) (with S1 ‫؍‬ SBG) for some special value of q 1 to be the one which is extensive [i.e., S q (N) ؔ N for N 3 ؕ]. Another concept which is relevant is strict or asymptotic scale-freedom (or scale-invariance), defined as the situation for which all marginal probabilities of the N-system coincide or asymptotically approach (for N 3 ؕ) 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 1, and not SBG, the entropy which matches standard, clausius-like, prescriptions of classical thermodynamics.

Zenodo (CERN European Organization for Nuclear Research), Sep 28, 2000

A dynamical systems based model of computation is studied. We demonstrate the computational capab... more A dynamical systems based model of computation is studied. We demonstrate the computational capability of a class of dynamical systems called switching map systems. There exists a switching map system with two t ypes of baker's map to emulate any T uring machines. The baker's maps are corresponding to the elementary operations of Turing machines such as left right head-moving and read write symbols. A connection between the generalized shifts by C. Moore Moore 91 and the inputoutput mappings by L. Blum et al. Blum, Cucker, Shub and Smale 98 is shown with our model. We present four concrete examples of switching map systems corresponding to the Chomsky hierarchy. T aking non-hyperbolic mappings as elementary operations, it is expected that the switching map systems shows a new model of computation with nonlinearity as an oracle.

Chaos, Oct 1, 2020

It has been shown that a permutation can uniquely identify the joint set of an initial condition ... more It has been shown that a permutation can uniquely identify the joint set of an initial condition and a non-autonomous external force realization added to the deterministic system in given time series data. We demonstrate that our results can be applied to time series forecasting as well as the estimation of common external forces. Thus, permutations provide a convenient description for a time series data set generated by non-autonomous dynamical systems.

RePEc: Research Papers in Economics, Sep 1, 2001

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attem... more We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her͞his 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 twoperson 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.

Physica D: Nonlinear Phenomena, 2021

In order to elucidate the plateau phenomena caused by vanishing gradient, we herein analyse stabi... more In order to elucidate the plateau phenomena caused by vanishing gradient, we herein analyse stability of stochastic gradient descent near degenerated subspaces in a multi-layer perceptron. In stochastic gradient descent for Fukumizu-Amari model, which is the minimal multi-layer perceptron showing non-trivial plateau phenomena, we show that (1) attracting regions exist in multiply degenerated subspaces, (2) a strong plateau phenomenon emerges as a noise-induced synchronisation, which is not observed in deterministic gradient descent, (3) an optimal fluctuation exists to minimise the escape time from the degenerated subspace. The noise-induced degeneration observed herein is expected to be found in a broad class of machine learning via neural networks.

In this paper, we discuss robust computation represented by collective motion of large neural dyn... more In this paper, we discuss robust computation represented by collective motion of large neural dynamics. There exist stable traveling bumps and their collisions in a two dimensional neural field. By using the stable traveling bumps and their collisions, arbitrary logical operations can be constructed. The resulting computation processes in the neural field is structurally and orbitally stable and the basin measure of the dynamics of the computations is finitely positive. Thus, the computations are robust and constructive in the framework of dynamical systems theory.

IEICE Proceeding Series, 2014

A random dynamical systems model is studied to understand coupled dynamics of auditory area and m... more A random dynamical systems model is studied to understand coupled dynamics of auditory area and motor area modulated by external force. We measure transfer entropy of coupled oscillators with the presence of noise to explain results of human brain wave experiments.

arXiv (Cornell University), Nov 9, 2018

The emergence of noise-induced chaos in a random logistic map with bounded noise is understood as... more 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.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022

We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a... more We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a class of one-dimensional random dynamical system with additive noise. The result is achieved with the help of rigorous computer assisted estimates. We first approximate the stationary distribution of the random dynamical system and then compute certified error intervals for the Lyapunov exponent. We find that the sign of the Lyapunov exponent changes at least three times when increasing the noise amplitude. We also show numerical evidence that the standard non-rigorous numerical approximation by finite-time Lyapunov exponent is valid with our model for a sufficiently large number of iterations. Our method is expected to work for a broad class of nonlinear stochastic phenomena.

arXiv: Dynamical Systems, 2018

In this paper, we show that under a generic condition of the coefficient of a stochastic phase os... more In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is always negative. Consequently, the generated random dynamical system exhibits a synchronization.

Theoretical and applied mechanics Japan, 2011

Earth System Dynamics Discussions, 2018

We derive a minimal dynamical model for the northern hemisphere mid-latitude jet dynamics by embe... more We derive a minimal dynamical model for the northern hemisphere mid-latitude jet dynamics by embedding atmospheric data, and investigate its properties (bifurcation structure, stability, local dimensions) for different atmospheric flow regimes. We derive our model according to the following steps: i) obtain a 1-D description of the mid-latitude jet-stream by computing the position of the jet at each longitude using the ERA-Interim reanalysis, ii) use the embedding procedure to derive a map of the local jet position dynamics, iii) introduce the coupling and stochastic effects deriving from both atmospheric turbulence and topographic disturbances to the jet. We then analyze the dynamical properties of the model in different regimes: i) one that gives the closest representation of the properties extracted from real data, ii) one featuring a stronger jet (strong coupling), iii) one featuring a weaker jet (low coupling), iv) modified topography. We argue that such a simple model provides a useful description of the dynamical properties of the atmospheric jet.

Nonlinear Theory and Its Applications, IEICE, 2016

Information flow in adaptively interacting stochastic processes is studied. We give an extended f... more Information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for interacting Markovian processes and compute a measure of causal information flow, which is different from the transfer entropy. In the game theoretic situation, causal information flow can show oscillatory behavior through reward-maximizing adaptation of two players. The adaptive dynamics for the coin-tossing game is exemplified and the causal information flow therein is investigated.

Unconventional Models of Computation, UMC’2K, 2001

Abstract. A dynamical systems based model of computation is studied, and we demonstrate the compu... more Abstract. 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 ...

Europhysics News, 2005

I t is our pleasure to welcome Jean Pierre Boon and Constantino Tsallis as guests Editors for the... more I t is our pleasure to welcome Jean Pierre Boon and Constantino Tsallis as guests Editors for the present Special Issue of Europhysics News on "Nonextensive Statistical Mechanics". They did a great job not only in selecting an impressive set of distinguished authors but also in writing the introductory Editorial and in each being a co-author of one of the contributions. The subject is difficult and could not go without a higher proportion of equations than usual in EPN: our thanks go to the EPN designer who had to face a heavier task than usual. It is sometimes necessary to address arduous developments to cover recent progress in Physics. This time, EPN will ask its readers to make an effort. It is always rewarding. The guests Editors were so efficient that the collected material passes largely the size of a standard EPN issue. We are grateful to the Publisher for accepting to accommodate all the articles in a single volume. It will make of this Special Issue the general reference work on "nonextensive statistical mechanics". Back to the usual mix of wide-ranging Features and News next time! The Editors

Physics Letters A, 2011

We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initi... more We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initial conditions, entropy production, and escape rate, in zlogistic 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.

AIP Conference Proceedings, 2000

ABSTRACT We first study here a simple stochastic dynamical equation with delayed self-feedback. T... more ABSTRACT We first study here a simple stochastic dynamical equation with delayed self-feedback. The model is investigated numerically and we find that its dynamics show an emergent regular ``spiking'' behavior, by ``tuning'' its ``noise'' and ``delay''. In order to gain insight into this ``resonance'', we abstract the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this abstracted model we can analytically capture the time interval histograms between spikes, and discover how the resonance between noise and delay arises. The resonance is also observed when such stochastic binary elements are coupled through delayed interaction. .

A random dynamics is extracted from time series of laminar-turbulent transition in rotating fluid... more A random dynamics is extracted from time series of laminar-turbulent transition in rotating fluid in an open cylinder. We focus on the dynamics of the surface height in the central region and measure switching dynamics between different quasi-stationary states and intensity of underlying turbulence. Density of return map is constructed from an one dimensional map with an stochastic term from the experimental data. It is shown that the random dynamics whose noise amplitude depends on the slow variable describes the observed macroscopic features of rotating fluid in terms of noise-induced phenomena.

IEICE Proceeding Series, 2014

A random dynamics with two stochastic terms is modeled based on a time series of physiological ex... more A random dynamics with two stochastic terms is modeled based on a time series of physiological experimental data to study synchrony between human heartbeats and pedaling rhythms modulated by music. We investigate reproduced time series, rotation numbers, and invariant densities in the model to explain transitory stagnation motion of synchrony in the experiments.

Starting with a group of reinforcement-learning agents we derive coupled replicator equations tha... more 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.