Complicated dynamics in planar polynomial equations

TL;DR

This paper investigates the complex chaotic behavior in planar polynomial differential equations by analyzing the interplay of periodic solutions and establishing the existence of numerous heteroclinic connections, linking chaos measurement to topological entropy.

Contribution

It introduces a mechanism for distributional chaos in nonautonomous planar ODEs and proves the existence of infinitely many heteroclinic solutions between periodic orbits.

Findings

Existence of distributional chaos in planar nonautonomous ODEs

Presence of infinitely many heteroclinic solutions between periodic solutions

Chaosity quantified via topological entropy

Abstract

We deal with a mechanism of generating distributional chaos in planar nonautonomous ODEs and try to measure chaosity in terms of topological entropy. It is based on the interplay between simple periodic solutions. We prove the existence of infinitely many heteroclinic solutions betwen the periodic ones.