Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations

TL;DR

This paper establishes an upper bound on the number of limit cycles in a nongeneric quadratic reversible system with discontinuous perturbations, using Picard-Fuchs equations and Chebyshev space properties.

Contribution

It introduces a novel approach combining Picard-Fuchs equations and Chebyshev space theory to analyze limit cycles in discontinuous quadratic reversible systems.

Findings

Upper bound for limit cycles with degree n perturbations

Application of Picard-Fuchs equations to discontinuous systems

Use of Chebyshev space properties in bifurcation analysis

Abstract

By using the Picard-Fuchs equation and the property of Chebyshev space to the discontinuous differential system, we obtain an upper bound of the number of limit cycles for the nongeneric quadratic reversible system when it is perturbed inside all discontinuous polynomials with degree $n$.