Some lattice models with hyperbolic chaotic attractors

TL;DR

This paper explores one-dimensional lattice models exhibiting hyperbolic chaotic attractors, with potential applications in designing robust electronic chaos generators and educational demonstrations.

Contribution

It introduces lattice models with spatially scaled patterns and Smale-Williams attractors, linking theoretical chaos with practical electronic and mechanical systems.

Findings

Patterns of different spatial scales arise alternately.

Spatial phase undergoes transformation via expanding circle map.

Models can serve as basis for robust chaos generators.

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.