Exponential Outer Synchronization between Two Uncertain Time-Varying Complex Networks with Nonlinear Coupling

Yongqing Wu,Li Liu

doi:10.3390/e17053097

Abstract

This paper studies the problem of exponential outer synchronization between two uncertain nonlinearly coupled complex networks with time delays. In order to synchronize uncertain complex networks, an adaptive control scheme is designed based on the Lyapunov stability theorem. Simultaneously, the unknown system parameters of uncertain complex networks are identified when exponential outer synchronization occurs. Finally, numerical examples are provided to demonstrate the feasibility and effectiveness of the theoretical results.

Highlights

Over the last decade, complex networks have received a great deal of interests from various research communities due to its wide applications in many fields including physics, mathematics, biology, engineering, social science and so on [1,2]
In [17], an adaptive feedback scheme was proposed to stabilize the synchronous solution of uncertain complex dynamical network with delayed coupling
This paper mainly focuses on the outer synchronization between two dynamical networks with unknown parameters and the system dynamic model can be involved in the designing of the controller

Summary

Introduction

Complex networks have received a great deal of interests from various research communities due to its wide applications in many fields including physics, mathematics, biology, engineering, social science and so on [1,2]. In [17], an adaptive feedback scheme was proposed to stabilize the synchronous solution of uncertain complex dynamical network with delayed coupling. Xu et al proposed an approach to identify the topological structure and unknown parameters for uncertain general complex networks with non-derivative and derivative couplings [35]. Wu and Lu investigated the outer synchronization between two uncertain time-varying dynamical networks with same topological structures [40]. Inspired by the above discussions, we investigate exponential outer synchronization and parameter identification between two uncertain time-varying complex dynamical networks with nonlinear coupling, time delays and different topological structures. Based on the Lyapunov stability theorem, an adaptive control scheme is proposed to achieve exponential outer synchronization between drive and response networks.

Problem formulation and preliminaries

Theoretical Results

Numerical Example

Conclusions