Finite cyclicity of quadratic slow-fast Darboux systems with a two-saddle loop

TL;DR

This paper proves that quadratic slow-fast Darboux systems with a two-saddle loop have a finite and uniformly bounded cyclicity, advancing understanding of their bifurcation behavior.

Contribution

It establishes the finite cyclicity of a specific class of quadratic slow-fast Darboux systems with a double heteroclinic loop, a novel result in the field.

Findings

Cyclicity is finite for the systems studied.

Cyclicity is uniformly bounded across the class.

Provides new insights into bifurcations of slow-fast systems.

Abstract

We prove that the cyclicity of a quadratic slow-fast integrable system of Darboux type with a double heteroclinic loop is finite and uniformly bounded.