Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

TL;DR

This paper introduces a generic Lyapunov-based method to achieve various types of synchronization in large, complex networks of time-delayed chaotic systems, extending previous work to more general and larger network structures.

Contribution

It generalizes synchronization techniques to complex networks with time-delayed chaotic nodes, removing previous limitations of linearity and small network size.

Findings

Successfully synchronized Ikeda and Mackey-Glass systems on Erdos-Renyi networks.

Derived stability conditions for projective-anticipating, projective, and projective-lag synchronization.

Validated the method through numerical examples demonstrating effective synchronization.

Abstract

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we can realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed by a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial-linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks and find both the existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.