Li-Yorke chaos in hybrid systems on a time scale

TL;DR

This paper proves the presence of Li-Yorke chaos in dynamic equations on time scales using reduction techniques, marking the first such demonstration in the literature, with an illustrative Duffing equation example.

Contribution

It introduces the first rigorous proof of chaos in dynamic equations on time scales using reduction techniques and Li-Yorke's definition.

Findings

Chaos is established in dynamic equations on time scales.

Reduction techniques effectively demonstrate chaos in DETS.

An illustrative Duffing equation example supports the theoretical results.

Abstract

By using the reduction technique to impulsive differential equations [1], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.