Monday, 28 September
10:00-10:45 Yuzuru Sato (Hokkaido University) A new characterization of noise-induced order
Noise-induced order (NIO) is a paradigmatic example of nontrivial noise-induced phenomena, characterized by pronounced spectral peaks and pseudoperiodic dynamics. We show that this periodicity is governed by the Ruelle-Pollicott resonances of the annealed transfer operator, independently of dynamical stability. Exact results for an analytically solvable model and numerical results for a modified Lasota--Mackey map show excellent agreement between resonance-based predictions and empirical power spectra across a broad range of noise amplitudes. Independent transitions in stability, diagnosed by the Lyapunov exponent, and statistical periodicity, diagnosed by the Ruelle-Pollicott resonances, give rise to three distinct types of NIO.
11:00-11:45 Isaia Nisoli (UFRJ/Hokkaido University) Transfer operators and Ruelle–Pollicott resonances in noise-induced order
Noise-induced order (NIO) is a striking phenomenon in random dynamical systems, where increasing additive noise induces spectral organization and pseudoperiodic dynamics. Recent work with Yuzuru Sato shows that this statistical periodicity is controlled by the Ruelle–Pollicott resonances of the annealed transfer operator—independent of dynamical stability. Through both exact results on analytically solvable models and numerical studies of the modified Lasota–Mackey map, we demonstrate that resonance-based predictions align with empirical power spectra across a broad range of noise amplitudes. I will focus on the mathematical machinery underlying this picture: transfer operator theory, spectral enclosure methods, and how Ruelle–Pollicott resonances encode the long-time behavior. Crucially, independent transitions in stability (diagnosed by Lyapunov exponents) and statistical periodicity (diagnosed by R-P resonances) give rise to three distinct types of NIO. I will explain how we rigorously certify these resonances and their role in the observable phenomena that Yuzuru will discuss phenomenologically.
14:00-14:45 Hisayoshi Toyokawa (Kitami Institute of Technology), Asymptotic constrictivity and mixing invariant measures
The notion of constrictivity, introduced by Lasota-Li-Yorke and developed by Komorn\’{i}k, characterizes the existence and finiteness of ergodic absolutely continuous invariant probability measures whose tail algebra is atomic with respect to the reference measure. Asymptotic constrictivity was recently introduced in the authors’ previous work and was naively expected to characterize the existence and finiteness of ergodic absolutely continuous invariant probability measures whose mixing components are also finite. In this talk, we see that this is indeed true for the case of Perron-Frobenius operators. Furthermore, a slightly weaker notion of asymptotic constrictivity is shown to be equivalent to the finitude of partially mixing invariant probability measures.
15:00-15:45 Fumihiko Nakamura (Kitami Institute of Technology), Toward a stability analysis of the density-dependent tent map
In the theory of autonomous evolution of densities, it is well known that iterating a Frobenius–Perron operator or a Markov operator typically drives the density either to a stationary state or to asymptotically periodic behavior. For non-autonomous evolutions, by contrast, in which a different map is applied at each step, one may expect richer and more complex density dynamics. In this talk we consider one such non-autonomous model, the "density-dependent tent map," proposed by Lasota and Mackey, in which the map itself varies according to the current density. This is a system in which the density evolves depending on a functional of the density itself, and in recent years it has come to be studied within the framework of self-consistent transfer operators, or nonlinear Markov operators. Regarding this system as a dynamical system on an extended space that simultaneously updates the parameter and the density, we present our attempt to analyze the stability of its fixed point. This is joint work with M. C. Mackey, M. Tyran-Kamińska, and U. Ernst.
16:00-16:45 Yuto Nakajima (DoshishaUniversity) Exact dimensionality of projected measures for expanding rational semigroups
We study the dimension theory of expanding rational semigroups from the viewpoint of random complex dynamics. Such a system can be naturally represented by a skew product over a symbolic dynamical system, where each symbolic sequence determines a non-autonomous composition of rational maps on the Riemann sphere. For an invariant Borel probability measure of the skew product, we consider its disintegration over a symbolic factor and investigate the push-forwards of the resulting conditional measures onto the Riemann sphere. We establish a Ledrappier--Young type dimension formula for these projected conditional measures. In particular, when the invariant measure is ergodic, the projected conditional measures are exact dimensional for almost every fiber. As a special case, by taking the trivial factor, we obtain the exact dimensionality of the projected invariant measure. These results provide a dimension-theoretic framework for measures arising in expanding random and non-autonomous complex dynamical systems.
Tuesday, 29 September
10:00-10:45 Kouji Yano (Osaka University) The law of large numbers for time-inhomogeneous Markov chains under general conditions
The strong law of large numbers for time-inhomogeneous Markov chains is studied under general conditions. Assuming Drift Condition together with a time-inhomogeneous Doeblin minorization, we develop a Nummelin-type splitting and obtain a strong law of large numbers. Our results utilize the invariant measure family in the sense of Liu--Lu (2025), and extend the classical Harris-ergodic LLN to the time-inhomogeneous setting.
11:00-11:45 Tomoki Inoue (Ehime University) Position dependent random maps with stochastically small entrances to the neighborhoods of fixed points
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. The selection of transformations is according to a probability density function which may depend on the position in the state space. We mainly consider piecewise monotonic random maps from [0, 1] to [0, 1] with the fixed point 0. In the case when the entrances to the small neighborhood of the fixed point 0 are stochastically small, we study the estimates of absolutely continuous invariant measures of random maps.
14:00-14:45 Takayuki Watanabe (Chubu University) Criteria for typical total disconnectedness of Julia sets of general random polynomials
I will discuss Julia sets arising from random iterations of polynomial maps, focusing on conditions that guarantee total disconnectedness. I will present sufficient conditions under which the random Julia set is almost surely totally disconnected, and illustrate the results with concrete examples. The talk will emphasize how randomness can produce geometric behavior that is qualitatively different from that of the corresponding deterministic systems.
15:00-15:45 Hiroki Sumi (Kyoto University) Random dynamical systems of polynomial automorphisms of $\Bbb{C}^{N}$
TBA
16:00-16:45 Takehiko Morita (Otemon Gakuin University) Random dynamical systems with noninvertible noise
This is a continuation of my presentation titled ¥lq Ergodic properties of random dynamical systems via natural extensions of noise transformations¥rq at the RIMS Conference in 2021. At that time, my attempt to establish an approach via natural extensions was far from satisfactory. In this talk, I would like to report on several improvements, including results on the weak-mixing property of random dynamical systems. If time permits, I would also like to touch upon a topic related to the quenched central limit theorem.
Wednesday, 30 September
10:00-10:40 Sosuke Ito (University of Tokyo) Thermodynamic trade-off relations on limit cycles
TBA
10:50-11:30 Takuma Akimoto (Tokyo University of Science) Infinite-Measure Dynamics in Confined Heterogeneous Diffusion: A Transition in the Moment
Heterogeneous diffusion processes can possess a non-normalizable infinite invariant density even in a bounded domain. Here, we study a confined generalized geometric Brownian motion whose diffusivity vanishes at the origin. By mapping the dynamics onto a Bessel process with a reflecting boundary, we derive the long-time behavior of the propagator. We show that different spatial regions govern different moments, leading to a transition in the spectrum of relaxation exponents: low-order moments exhibit an order-dependent decay, whereas high-order moments share a common decay exponent determined by the infinite invariant density. The transition is controlled by an integrability threshold of the moments. These results demonstrate how infinite-measure dynamics gives rise to anomalous relaxation in confined stochastic systems.
11:40-12:00 Keisuke Taga (Tokyo University of Science) Pattern Formation and Phase Transitions in a Stochastic Tape-Peeling Model
TBA
14:00-14:10 Yuzuru Sato (Hokkaido University) Introduction
I will talk about an overview for problems in dynamical systems with large degrees of freedom from a viewpoint of random and non-autonomous dynamical systems.
14:10-14:30 Isaia Nisoli (UFRJ/Hokkaido University) Rigorous computation for nonlinear transfer operators of coupled maps
TBA
14:50-15:30 Jin Yan (Weierstrass Institute Berlin ) Basin metamorphosis in coupled phase oscillators
We investigate the global basin structure of twisted states in nearest-neighbor coupled phase oscillators with a common phase shift α. As α increases, basin boundaries become progressively more complex, with their fractal dimension growing toward that of the full ambient phase space. We conjecture that the basins eventually become riddled-like as the system approaches the limit α→π/2, where the dynamics becomes volume-preserving. We characterize the transient dynamics via the stabilization time of the winding number and demonstrate that it grows with system size. The scaling accelerates at larger phase shifts, transitioning from logarithmic to power-law behavior. We further analyze the dynamical origin of these long transients. Our results demonstrate how a single phase-shift governs fractal basin complexity and provide new insights into the global geometry and transient dynamics of multistable, yet non-chaotic, coupled phase oscillators.
15:40-16:20 Ayumi Ozawa (JAMSTEC) Transitions in Coupled Oscillators subject to Stochastic Resetting
Turnover—the replacement of old components with new ones—is ubiquitous in open systems composed of many interacting units. Here, we incorporate turnover into a population of coupled phase oscillators by modeling the replacement of oscillators as stochastic phase resetting. We find that collective oscillations disappear through two distinct transitions depending on both the coupling strength and turnover rate: desynchronization and what we term "stochastic oscillation quenching." Importantly, stochastic oscillation quenching cannot be induced by turnover or coupling alone, but arises from their interplay. We obtain the transition curves through mean-field analysis and confirm them numerically.
Thursday, 1 October
10:00-10:40 Jun-nosuke Teramae (Kyoto University) Stochastic dynamics of memory representation in the brain
Neural populations that are selectively activated by events experienced by an animal are believed to provide a stable substrate for memories of the animal’s experiences in the brain. However, recent advances in longitudinal recordings of large neuronal populations have revealed that the receptive fields of individual neurons continuously and stochastically drift over time. This phenomenon, known as representational drift, was first reported in the hippocampus and has since been observed across widespread brain regions. Yet the mechanisms underlying representational drift and its functional significance remain largely unclear. Here, based on a recently proposed Bayesian framework describing the stochastic properties of neurons and synapses, we develop a theoretical model that reproduces key features of representational drift. Importantly, the theory further demonstrates that representational drift enables a neural network to extend its representation to newly encountered environments while preserving previously acquired memories. Our results suggest that representational drift provides a mechanism for balancing the stability and plasticity of memory representations in the brain.
10:50-11:30 Tsuyoshi Chawanya (Osaka University) Direct transition from torus to chaos via a pseudo on-off intermittency on the quasi-periodically driven logistic map system
TBA
11:40-12:00 Eiki Kojima (Hokkaido University) Noise-induced transient chaos in dissipative magnetic pendulums
TBA
14:00-14:40 Tetsuro Konisi (Chubu University) Normal-Mode Analysis and Stability of a Multiple Pendulum
保存力学系において、相空間内で規則的な運動が生じる領域が、自由度を大きくするにつれてどのように変化するかは興味深い問題である。我々は、多重振り子の基準振動がラゲール多項式で書けることを用いて、基準振動間のエネルギー交換が生ずる臨界エネルギーの値の自由度依存性を数値的に調べた。その結果、数値計算の範囲内ではあるが、自由度を大きくしても臨界エネルギーがゼロにならず、有限の値でとどまる子例を見出した。このことは、あるクラスの力学系では、自由度が巨視的になってもカオス化しない初期条件が有限に残る可能性を示唆している。
（柳田達雄氏（大阪電気通信大学）との共同研究）
14:50-15:10 Miki Kobayashi (Rissho University) Attractors of High-Dimensional Neural Network Dynamics in Reservoir Computing
TBA
15:30-16:10 Masanobu Inubushi (Tokyo University of Science) Generalized synchronization in reservoir computing for bifurcation prediction
A bifurcation in a dynamical system refers to a qualitative change in the behavior of its solutions caused by variations in system parameters. Bifurcation phenomena arise in nonlinear models describing a wide range of physical, meteorological, and engineering systems. Predicting and reconstructing post-bifurcation dynamics using only pre-bifurcation data is an important challenge in machine learning applications. Reservoir Computing (RC) is a machine learning framework widely used for reconstructing dynamical systems from time-series data. By mapping input signals into a high-dimensional nonlinear space, RC effectively captures complex temporal structures while maintaining both computational efficiency and stable training. In this study, inspired by the bifurcation prediction method proposed by Kim et al. (Nature Machine Intelligence, 2021) and the transfer learning framework introduced by Inubushi and Goto (Physical Review E, 2020), we demonstrate that bifurcation prediction can be achieved by linearly interpolating two pretrained readout matrices by using RC with an interpolation coefficient. Furthermore, by introducing the Kullback–Leibler divergence (KLD) as a performance metric, we clarify the relationship between the interpolation coefficient and the system parameter. The proposed method is shown to reconstruct post-bifurcation dynamics with accuracy comparable to or exceeding that of the conventional approach.
16:20-17:00 Masahiro Morikawa (RIKEN), Cross-Scale Dynamics of Amplitude-Modulated High-Dimensional Synchronized Systems: 1/f Fluctuations, Power Laws, and Taylor’s Law
多数の局所振動子・循環が同期と脱同期を繰り返すと、うなりとして遅い包絡変動が生じ、復調された観測量に1/f型スペクトル、冪則的バースト階層、Taylor則/rms-flux関係が現れる。本講演では、この振幅変調機構を、蔵本モデル，古典スピンモデル，結合ローレンツモデルなどで共通原理として扱い，太陽フレア、経済時系列、ブラックホール降着流に共通するスケール横断的力学として議論する。
Friday, 2 October
10:00-10:40 Toshitaka Saiki (Hitotsubashi University) Finite-Time Targeting Control in Weakly Stable Dissipative Systems -- Spontaneous Transition of Optimal Perturbation Patterns --
Understanding finite-time sensitivity is central to high-dimensional dissipative systems, from fluid dynamics to atmospheric science, where direct control remains a fundamental challenge. While classical optimal perturbation theory focuses on maximal growth problems, many realistic interventions are inherently directional: the objective is to steer a system to a prescribed target state in finite time using a limited initial perturbation. In this talk, I present a study of finite-time targeting in weakly stable dissipative systems. Using a spatially extended coupled map lattice as a toy model for Rayleigh–Bénard convection, we demonstrate that varying only the allowable magnitude of the initial perturbation induces a sharp qualitative transition in the structure of optimal perturbations. The optimal patterns switch abruptly from spatially ordered (coherent) structures to highly complex (incoherent) ones. We show that the coherent regime can be understood analytically through a linearized formulation of the finite-time targeting problem. The optimal perturbation is characterized by a singular value decomposition of the finite-time evolution operator, revealing that non-leading singular modes can dominate optimality because they align with the target. Beyond a critical perturbation magnitude, however, linear predictability breaks down. In this regime, nonlinear phase-space geometry becomes relevant for shaping optimal perturbations, in particular through the influence of basin boundaries associated with unstable invariant states, even in the absence of actual basin switching. More broadly, this work highlights a generic mechanism: when objectives are directional, and interventions are small, optimal influence is governed as much by geometry as by growth.
This is a joint work with Natsuki Tsutsumi, Hibiki Kato, Masato Hara, Miki U. Kobayashi, and Tatsuo Yanagita.
10:50-11:30 Tatsuo Yanagita (Osaka Electro-Communication University) A Coupled Map Lattice Approach to Tropical Cyclone Dynamics
We propose a coupled map lattice (CML) model to investigate tropical cyclone dynamics. Rather than reproducing detailed atmospheric processes, our aim is to capture the essential mechanisms of structural formation using a minimal dynamical model. Numerical simulations demonstrate the emergence of vortex and spiral structures and their transitions with changing model parameters.
11:40-12:20 Hiromichi Suetani (Oita University) Gap between the prediction optimum and the edge of conditional stability in infinite-size echo state networks: A recurrent kernel approach
Echo state networks (ESNs) achieve optimal prediction of chaotic time series at recurrent coupling strengths below the edge of conditional stability. We investigate whether this gap is a finite-size effect using the recurrent kernel machine (RKM), the infinite-size limit of an ESN with error-function activation and Gaussian weights. For the Mackey–Glass equation, Hénon map, and Lorenz-96 model, finite ESN errors and optimal coupling strengths approach their RKM counterparts as network size increases, but the RKM optimum remains below the edge. The gap therefore persists at infinite size and depends on training-set size, regularization, and sampling interval of the chaotic time series. Below the optimum, prediction error is governed by regularization, and between the optimum and the edge, it is governed by training-set size. The optimum approaches the edge as training-set size increases and moves away as regularization weakens. Larger sampling intervals widen the gap even at fixed prediction time. Near the edge, the Hölder exponent of the generalized synchronization function decreases to unity or below, with a sampling-dependent onset, consistent with the dependence of prediction error on data availability.
13:30-14:10 Yoshiyuki Yamagichi (Kyoto University) Non-mean-field response and fluctuation in thermal equilibrium of mean-field systems
Mean-field systems in thermal equilibrium are generally thought to be analyzed by using statistical mechanics. However, when the system is evolved according to the Hamiltonian equations of motion, it exhibits numerous anomalies in its response and fluctuations. We demonstrate anomalous critical exponents in the response and anomalous fluctuations in thermal equilibrium state with a theory that accounts for them.
14:20-15:00 Kiyoshi Kanazawa (Kyoto University), Stochastic thermodynamics for non-Markov jump processes: Zwanzig jump models and their thermodynamic structure
Stochastic thermodynamics investigates energetic and entropic bounds in small systems. Foundational results, e.g., the first and second laws, predominantly rely on the Markov (memoryless) assumption. Although physicists recognise that the Markov assumption is questionable in real experimental setups, extending stochastic thermodynamics to general non-Markov systems has proven challenging. Here we establish stochastic thermodynamics for classical non-Markov jump processes with equilibrium bath degrees of freedom. We introduce a key technique, called the Fourier embedding (or Markov lifting), which converts non-Markov jump processes into Markovian field dynamics of auxiliary Fourier modes. This yields necessary and sufficient conditions for time-reversal symmetry and enables the derivation of the second law for a broad class of strong-memory dynamics that admit the Fourier embedding. We demonstrate the power of our framework by presenting two novel non-Markov models: (i) a history-dependent two-state model and (ii) a history-dependent random walk. These models are jump-process counterparts of the classical Zwanzig models originally for the generalized Langevin equation.