Period-doubling route to chaos in driven impulsive systems

TL;DR

This paper investigates how impulsive differential equations driven by chaotic systems exhibit chaos themselves, demonstrating that impulsive responses can mirror the chaos of the driving system through theoretical proofs and simulations.

Contribution

It provides a rigorous proof that impulsive systems driven by chaos are also chaotic, highlighting the presence of sensitivity and unstable periodic motions.

Findings

Impulsive driven systems are chaotic if the driving system is chaotic.

Theoretical proofs confirm chaos in impulsive systems.

Simulations support the analytical results.

Abstract

In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsive system is also chaotic. Our results are based on the presence of sensitivity and infinitely many unstable periodic motions. The theoretical results are supported by simulations.