Lag synchronization and scaling of chaotic attractor in coupled system

TL;DR

This paper introduces a delay coupling method for achieving lag synchronization in chaotic oscillators, allowing control over the lag and scaling of attractors, with practical electronic circuit implementation.

Contribution

It presents a novel delay coupling design that enables precise lag synchronization and attractor scaling in chaotic systems, supported by numerical and experimental validation.

Findings

Successful delay coupling in various chaotic systems

Ability to scale attractors during lag synchronization

Electronic circuit implementation of the proposed method

Abstract

We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott system and, a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.