The maximal number of limit cycles in a family of polynomial systems

TL;DR

This paper investigates the maximum number of limit cycles that can occur in a family of polynomial systems using bifurcation techniques to understand their global bifurcation behavior.

Contribution

It provides a new upper bound on the number of limit cycles in polynomial systems through bifurcation analysis, advancing the understanding of their dynamic complexity.

Findings

Established the maximal number of limit cycles in the studied family.

Applied bifurcation methods to analyze global bifurcations.

Enhanced the theoretical understanding of polynomial system dynamics.

Abstract

The main objective of this paper is to study the number of limit cycles in a family of polynomial systems. Using bifurcation methods, we obtain the maximal number of limit cycles in global bifurcation.