Replication of Period-Doubling Route to Chaos in Coupled Systems with Delay

TL;DR

This paper rigorously proves the replication of period-doubling chaos in coupled delay systems, introducing a new sensitivity definition and supporting results with simulations.

Contribution

It introduces a novel sensitivity replication concept and provides a rigorous proof of period-doubling cascade in coupled delay systems.

Findings

Replication of period-doubling cascade confirmed

New sensitivity definition applied successfully

Simulations support theoretical results

Abstract

In this study, replication of a period-doubling cascade in coupled systems with delay is rigorously proved under certain assumptions, which guarantee the existence of bounded solutions and replication of sensitivity. A novel definition for replication of sensitivity is utilized, in which the proximity of solutions is considered in an interval instead of a single point. Examples with simulations supporting the theoretical results concerning sensitivity and period-doubling cascade are provided.