Adaptive synchronization of the stochastic delayed RDNNs with unknown time-varying parameters

Weiyuan Zhang,Minglai Chen,Junmin Li

doi:10.1186/1687-1847-2013-253

Weiyuan Zhang, Minglai Chen + Show 1 more

Open Access

https://doi.org/10.1186/1687-1847-2013-253

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Abstract

This paper presents a new adaptive synchronization problem for the delayed reaction-diffusion neural networks (RDNNs) with unknown time-varying coupling strengths under stochastic perturbations. By constructing a differential-difference-type learning law and an adaptive learning control law, and using Lyapunov-Krasovskii-like composite energy functional method, a novel sufficient condition is derived to ensure adaptive asymptotical synchronization in the mean square sense for the addressed system. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Highlights

In recent decades, different types of neural networks (NNs) with time delays have been widely investigated due to their applicability in solving some image processing, signal processing automatic control engineering, fault diagnosis, telecommunications, and pattern recognition problems
The realistic applications heavily depend on the dynamical behaviors [ – ]
The analysis of the dynamical behaviors such as stability, periodic oscillation, bifurcation and chaos is a necessary step for practical design of NNs

Summary

Introduction

Different types of neural networks (NNs) with time delays have been widely investigated due to their applicability in solving some image processing, signal processing automatic control engineering, fault diagnosis, telecommunications, and pattern recognition problems. The analysis of the dynamical behaviors such as stability, periodic oscillation, bifurcation and chaos is a necessary step for practical design of NNs. For instance, in [ ], by utilizing the Lyapunov-Krasovkii functional and combining with the linear matrix inequalities (LMIs) approach, the authors analyzed the global exponential stability of neutral-type impulsive NNs. By constructing a newly augmented Lyapunov-Krasovskii functional, [ ] established less conservative stability criteria in the form of LMIs. Control and synchronization of chaotic systems have become an important topic since the pioneering work of Pecora and Carroll in [ ]. The synchronization for delayed NNs has been reported [ – ]

Objectives

Conclusion