Homoclinic and Heteroclinic Motions in Hybrid Systems with Impacts

TL;DR

This paper introduces a method to generate and prove the existence of homoclinic and heteroclinic motions in impulsive hybrid systems influenced by discrete maps, supported by simulations of a Duffing impact oscillator.

Contribution

It provides a rigorous proof of homoclinic and heteroclinic motions in impulsive systems driven by maps with such orbits, complemented by simulation validation.

Findings

Existence of homoclinic and heteroclinic motions in impulsive systems

Theoretical proof based on discrete map properties

Simulation results with a Duffing oscillator with impacts

Abstract

In this paper, we present a method to generate homoclinic and heteroclinic motions in impulsive systems. We rigorously prove the presence of such motions in the case that the systems are under the influence of a discrete map that possesses homoclinic and heteroclinic orbits. Simulations that support the theoretical results are represented by means of a Duffing equation with impacts.