Chaotic singular maps

TL;DR

This paper studies a family of singular maps that exhibit robust chaos, analyzing their transition boundaries and routes to chaos, highlighting their potential for reliable chaotic modeling.

Contribution

It introduces a simple model of singular maps demonstrating robust chaos and characterizes the critical boundaries and transition routes to chaos.

Findings

Critical boundaries for chaos and stability are calculated.

Transitions to chaos occur via type-I or type-III intermittency.

The maps are useful for reliable chaotic modeling and applications.

Abstract

We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. It is shown that the transitions to robust chaos in these systems occur either through the routes of type-I or type-III intermittency and the critical boundaries for each type of transition have been determined on the phase diagram of the system. The simplicity of these singular maps and the robustness of their chaotic dynamics make them useful ingredients in the construction of models and in applications that require reliable operation under chaos.