Center and isochronous center of a class of quasi-analytic switching systems

TL;DR

This paper investigates the dynamics of quadratic quasi-analytic switching systems, revealing complex behaviors including multiple limit cycles and providing explicit criteria for classifying centers and isochronous centers.

Contribution

It introduces an improved method for computing focus values and periodic constants, advancing the analysis of integrability and linearization in quasi-analytic switching systems.

Findings

Existence of six limit cycles near the origin.

Existence of seven limit cycles near infinity.

Explicit conditions for centers and isochronous centers.

Abstract

In this paper, we study the integrability and linearization of a class of quadratic quasi-analytic switching systems. We improve an existing method to compute the focus values and periodic constants of quasi-analytic switching systems. In particular, with our method, we demonstrate that the dynamical behaviors of quasi-analytic switching systems are more complex than that of continuous quasi-analytic systems, by showing the existence of six and seven limit cycles in the neighborhood of the origin and infinity, respectively, in a quadratic quasi-analytic switching system. Moreover, explicit conditions are obtained for classifying the centers and isochronous centers of the system.