Some lattice models with hyperbolic chaotic attractors

2019/09/03 by С. П. Кузнецов, Kuznetsov, Sergey P.
Economics, Econometrics and Finance · Mathematics · #37D20 #37D45 #70K75 #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical Dynamics and Fractals #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1909.01896

openalex publication_date 2019/09/03 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28

Abstract

Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies occurrence of Smale-Williams attractors in the multidimensional state space. These models can serve as a basis for design electronic generators of robust chaos within a paradigm of coupled cellular networks. One of the examples is a mechanical pendulum system interesting and demonstrative for research and educational experimental studies.

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