How to induce multiple delays in coupled chaotic oscillators?

TL;DR

This paper presents a method to induce multiple lag configurations in coupled chaotic oscillators, enabling different state variables to attain distinct time shifts, with practical implementation in electronic circuits.

Contribution

It introduces a novel coupling design that achieves multiple lag synchronization in coupled systems, demonstrated through numerical examples and physical circuit realization.

Findings

Successful induction of multiple lag configurations in chaotic systems

Numerical validation with Rössler and Hindmarsh-Rose models

Physical realization in electronic circuits

Abstract

Lag synchronization is a basic phenomenon in mismatched coupled systems, delay coupled systems and time-delayed systems. It is characterized by a lag configuration that establishes a unique time shift between all the state variables of the coupled systems. In this report, an attempt is made how to induce multiple lag configurations in coupled systems when different pairs of state variables attain different time shift. A design of coupling is presented to realize this multiple lag synchronization. Numerical illustration is given using examples of the R\"ossler system and the slow-fast Hindmarsh-Rose neuron model. The multiple lag scenario is physically realized in an electronic circuit of two Sprott systems.