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The problem of projective lag synchronization of coupled neural networks with time delay is investigated. By means of the Lyapunov stability theory, an intermittent controller is designed for achieving projective lag synchronization between two delayed neural networks systems. Numerical simulations on coupled Lu neural systems illustrate the effectiveness of the results.

In the past few years, synchronization of neural networks has been extensively investigated due to their successful application in many areas, such as communication, modeling brain activity, signal processing, and combinatorial optimization. There are several different synchronization schemes including complete, lag, projective, generalized, phase, and anticipated synchronization [

In this paper, we will deal with the analysis issue for projective lag synchronization of neural networks with time delay by intermittent control approach. Recently, we have employed this method to stabilize and synchronize chaotic systems [

In this paper, we consider the chaotic cellular neural networks described by

Consider the corresponding slave system given in the following form:

Let

Under the control of the form (

The master system (

This section addresses the projective lag synchronization problem of coupled neural networks.

Suppose that there exist constants

Then, the projective lag synchronization error system (

Consider the following Lyapunov function:

When

This implies that the projective lag synchronization error system (

This implies that the projective lag synchronization between the master system (

Let

Suppose that there exist positive scalars

If

It is clear that when the time delay vanishes, that is,

From Corollary

Note that

In this section, Lu neural oscillator [

Consider the Lu neural oscillator [

This model was investigated by Lu in [

From Theorem

Noting that

The chaotic attractor of the Lu oscillator described by (

The relationship between

The norm of synchronization error curve with

This paper addressed projective lag synchronization of coupled neural networks with time delay. Based on Lyapunov stability theory and adaptive control techniques, several criteria for projective lag synchronization of identical neural networks with time delay have been established. With the proposed method, the simulations of projective lag between coupled Lu systems have showed the effectiveness of theoretical result.

This publication was made possible by NPRP Grant no. NPRP 4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. This work was also supported by Natural Science Foundation of China (Grant no. 61374078), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ121505), the Natural Science Foundation Project of Chongqing CSTC (Grant no. cstc2011jjA40005).