Weak bi-center and critical period bifurcations of a $Z_2$-Equivariant quintic system

TL;DR

This paper investigates the bifurcation of critical periods in a symmetric quintic system, identifying the maximum number of bifurcations and analyzing the weak bi-center using symbolic and numerical methods.

Contribution

It provides the first detailed analysis of weak bi-centers and critical period bifurcations in a $Z_2$-equivariant quintic system, combining symbolic and numerical techniques.

Findings

Identified the order of the weak bi-center.

Determined the maximum number of bifurcating critical periods.

Used computer algebra and numerical analysis for precise results.

Abstract

With the help of computer algebra system-\textsc{Mathematica}, this paper considers the weak center problem and local critical periods for bi-center of a $Z_2$-Equivariant quintic system with eight parameters. The order of weak bi-center is identified and the exact maximum number of bifurcation of critical periods generated from the bi-center is given via the combination of symbolic calculation and numerical analysis.