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By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…

Chaotic Dynamics · Physics 2007-05-23 Michael Blank

The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…

chao-dyn · Physics 2008-02-03 F. Leyvraz , T. H. Seligman

In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…

Dynamical Systems · Mathematics 2007-05-23 Artur Avila , Carlos Gustavo Moreira

Chaos is popularly associated with its property of sensitivity to initial conditions. In this paper we will show that there can be a flip side to this property which is quite fascinating and highly useful in many applications. As a result,…

Chaotic Dynamics · Physics 2009-05-05 Prabhakar G. Vaidya

In 2016, Hou and Wang introduced the concept of multiple mappings based on iterated function system, which is an important branch of fractal theory. In this paper, we introduce the definitions of sensitivity, accessibility, and Kato's chaos…

Dynamical Systems · Mathematics 2024-06-21 Yingcui Zhao

A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…

Adaptation and Self-Organizing Systems · Physics 2009-11-07 Tatsuo Shibata , Kunihiko Kaneko

The Multiscale Law of Requisite Variety is a scientific law relating, at each scale, the variation in an environment to the variation in internal state that is necessary for effective response by a system. While this law has been used to…

Physics and Society · Physics 2018-12-04 Taeer Bar-Yam , Owen Lynch , Yaneer Bar-Yam

We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is…

Mathematical Finance · Quantitative Finance 2017-03-08 Y. Charles Li , Hong Yang

We revisit the globally coupled map lattice (GCML). We show that in the so called turbulent regime various periodic cluster attractor states are formed even though the coupling between the maps are very small relative to the non-linearity…

Chaotic Dynamics · Physics 2016-09-07 Tokuzo Shimada , Kengo Kikuchi

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…

Neurons and Cognition · Quantitative Biology 2025-03-25 Ábel Ságodi , Guillermo Martín-Sánchez , Piotr Sokół , Il Memming Park

The first part of this paper defines recursive interactions by means of logistic functions and derives a general result on the way interacting systems evolve in attractors. It also defines the notion of coevolution trajectory and presents a…

General Mathematics · Mathematics 2008-04-21 Antonio Leon

The predictability of weather and climate is strongly state-dependent: special and extremely relevant atmospheric states like blockings are associated with anomalous instability. Indeed, typically, the instability of a chaotic dynamical…

Chaotic Dynamics · Physics 2024-12-24 Chiara Cecilia Maiocchi , Valerio Lucarini , Andrey Gritsun , Yuzuru Sato

The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…

Dynamical Systems · Mathematics 2025-09-09 Kimberly Ayers , Ami Radunskaya

The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observational data. Yet the reliability of learned surrogates and…

Dynamical Systems · Mathematics 2025-11-13 Zakhar Shumaylov , Peter Zaika , Philipp Scholl , Gitta Kutyniok , Lior Horesh , Carola-Bibiane Schönlieb

We generate new hierarchy of many-parameter family of maps of the interval [0,1] with an invariant measure, by composition of the chaotic maps of reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently…

Chaotic Dynamics · Physics 2015-06-26 M. A. Jafarizadeh , S. Behnia , S. Khorram , H. Naghshara

A chaotic network of size $N$ with delayed interactions which resembles a pseudo-inverse associative memory neural network is investigated. For a load $\alpha=P/N<1$, where $P$ stands for the number of stored patterns, the chaotic network…

Chaotic Dynamics · Physics 2015-06-03 Y. Peleg , M. zigzag , W. Kinzel , I. Kanter

We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…

Quantum Physics · Physics 2021-03-02 Manik Kapil , Amarendra K. Sarma

One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional…

Chaotic Dynamics · Physics 2022-11-23 Jeremy P Parker , Tobias M Schneider

We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar H\'{e}non map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two…

Chaotic Dynamics · Physics 2023-06-08 Amanda E Hampton , James D Meiss

Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…

chao-dyn · Physics 2009-10-30 Awadhesh Prasad , Vishal Mehra , Ramakrishna Ramaswamy