Effect of noise on generalized synchronization of chaos: theory and experiment

TL;DR

This paper investigates how noise affects generalized synchronization in chaotic systems, demonstrating high stability under certain conditions through theoretical, numerical, and experimental analyses.

Contribution

It provides a comprehensive analysis of noise effects on generalized synchronization, combining theory, simulations, and experiments to reveal conditions for high stability.

Findings

Generalized synchronization remains stable under noise if attractors have large basins.

Modified system approach explains the stability reasons.

Experimental and numerical results confirm theoretical predictions.

Abstract

The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized synchronization is shown to possess a great stability with respect to noise. The reasons of the revealed particularity are explained by means of the modified system approach [A.E. Hramov, A.A. Koronovskii, Phys. Rev. E. 71, 067201 (2005)] and confirmed by the results of numerical calculations and experimental studies. The main results are illustrated using the examples of unidirectionally coupled chaotic oscillators and discrete maps as well as spatially extended dynamical systems. Different types of the model noise are analyzed. Possible applications of the revealed particularity are briefly discussed.