Degenerate resonances and their stability in planar systems with small negative divergence

TL;DR

This paper investigates the existence and stability of periodic solutions in planar conservative systems with small negative divergence perturbations, providing universal conditions that apply to various bifurcation scenarios.

Contribution

It introduces universal sufficient conditions for the existence and asymptotic stability of periodic solutions in systems with small negative divergence, regardless of bifurcation complexity.

Findings

Conditions for existence of periodic solutions

Criteria for asymptotic stability

Applicability to systems with degenerate bifurcations

Abstract

We consider a conservative system with small periodic perturbations under the assumption that the divergence of the perturbed system is negative. The main theorems provide universal sufficient conditions for the existence and asymptotic stability of periodic solutions that apply regardless of whether the zeros of the bifurcation function are simple or not.