Persistence of Chaos in Coupled Lorenz Systems

TL;DR

This paper investigates the persistent chaos in unidirectionally coupled Lorenz systems, showing that chaos remains despite synchronization attempts, with implications for weather modeling and laser systems.

Contribution

It provides a theoretical proof of chaos persistence and demonstrates the absence of synchronization using auxiliary systems and Lyapunov exponents.

Findings

Chaos persists in the response system regardless of synchronization.

Periodic motions are embedded within the chaotic attractor.

Results have implications for weather dynamics and coupled laser systems.

Abstract

The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and the auxiliary system approach and conditional Lyapunov exponents are utilized to demonstrate the absence of synchronization. Periodic motions embedded in the chaotic attractor of the response system is demonstrated by taking advantage of a period-doubling cascade of the drive. The obtained results may shed light on the global unpredictability of the weather dynamics and can be useful for investigations concerning coupled Lorenz lasers.