Langevin approach to synchronization of hyperchaotic time-delay dynamics

TL;DR

This paper introduces a Langevin equation-based analytical framework to understand synchronization in hyperchaotic delay systems, validated through simulations and applicable to communication and electro-optical devices.

Contribution

It presents a novel approach using Langevin equations to analytically characterize hyperchaotic synchronization phenomena, including effects of noise and parameter mismatch.

Findings

Langevin formalism accurately models hyperchaotic synchronization.

Synchronization deviations can be quantified with a similarity function.

Numerical simulations support the theoretical predictions.

Abstract

In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical properties of a class of hyperchaotic attractors can be reproduced with a linear Langevin equation, defined by replacing the non-linear delay force by a delta-correlated noise. Therefore, the synchronization phenomenon can be analytically characterized by a set of coupled Langevin equations. We apply this formalism to study anticipated synchronization dynamics subject to external noise fluctuations as well as for characterizing the effects of parameter mismatch in a hyperchaotic communication scheme. The same procedure is applied to second order differential delay equations associated to synchronization in electro-optical devices. In all cases, the departure with respect to perfect synchronization is measured through a similarity function. Numerical simulations in discrete maps associated to the hyperchaotic dynamics support the formalism.