Anticipatory synchronization with variable time delay and reset

TL;DR

This paper introduces a novel method for synchronizing chaotic systems using variable delay coupling with intermittent information exchange, applicable to systems like Rossler and Lorenz, with stability analysis and numerical validation.

Contribution

It presents a new synchronization approach with variable delay and reset intervals, enhancing control over chaotic systems with intermittent data exchange.

Findings

Successful synchronization demonstrated on Rossler and Lorenz systems.

Stability of the synchronization manifold confirmed through discrete error dynamics.

Method allows synchronization with intermittent information at fixed reset times.

Abstract

A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is realized with intermittant information about the driving system at intervals fixed by a reset time. The stability of the synchronization manifold is analyzed with the resulting discrete error dynamics. The numerical calculations in standard systems like the Rossler and Lorenz systems are used to demonstrate the method and the results of the analysis.