Limit cycles and chaos in planar hybrid systems
Jaume Llibre, Paulo Santana
TL;DR
This paper investigates planar hybrid systems with linear centers and polynomial resets, analyzing their limit cycles and demonstrating the existence of chaotic behavior within these systems.
Contribution
It introduces a comprehensive analysis of limit cycles and chaos in hybrid systems with polynomial reset maps, expanding understanding of their complex dynamics.
Findings
Existence of limit cycles in hybrid systems with polynomial resets
Examples of chaotic dynamics in such hybrid systems
Characterization of system behavior based on reset map degree
Abstract
In this paper we study the family of planar hybrid differential systems formed by two linear centers and a polynomial reset map of any degree. We study their limit cycles and also provide examples of these hybrid systems exhibiting chaotic dynamics.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems