Pinning Control for Synchronization of Drive-Response Memristive Neural Networks with Nonidentical Parameters

In this paper, the asymptotic synchronization for drive-response memristive neural networks(MNNs) with nonidentical parameters is investigated. Parameter inconformity is ubiquitous between drive and response systems due to environmental or internal influence. However, the majority of previous results were based on the well-matched MNNs. Thus, it is meaningful to study the synchronization problem of MNNs with nonidentical parameters. First, coefficient mismatches are dealt within the framework of set-valued maps and differential inclusions. Furthermore, in order to reduce the control cost, a pinning control strategy is adopted to drive two nonidentical MNNs to achieve asymptotic synchronization. And the sufficient stability conditions are given based on Lyapunov functional method. Finally, the effectiveness of proposed pinning controller is verified by a numerical example.

I. Introduction

Memristor was first proposed by Chua [1] in 1971, and it was predicted as the fourth basic circuit element besides resistor, inductor and capacitor. The memristor can describe the relationship of magnetic flux and electric charge, and it can memorize the quantity of charge even though the excitation source is turned off. About 40 years later, Hewlett-Packard company prototyped practical memristor within nanometer size in 2008, which was a landmark progress to manufacture new arithmetic operation unit or nonvolatile memory chipset [2].