Chaos in Saw Map

TL;DR

This paper investigates the chaotic behavior and attractors of a scalar piecewise linear 'saw map' with infinitely many segments, which models certain two-dimensional systems with saturation and hysteresis effects.

Contribution

It provides a detailed analysis of chaos and attractors in the saw map, linking it to systems with saturation functions and stop hysteresis operators, and exploring parameter-dependent dynamics.

Findings

Identification of chaotic sets and attractors in the saw map

Parameter conditions leading to chaos or regular behavior

Connection between the saw map dynamics and two-dimensional systems with hysteresis

Abstract

We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincar\'e map of simple two-dimensional discrete time piecewise linear systems involving a saturation function. Alternatively, these systems can be viewed as a feedback loop with the so-called stop hysteresis operator. We analyze chaotic sets and attractors of the "saw map" depending on its parameters.