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This paper is concerned with

Since the seminal work for Cohen-Grossberg neural networks by Cohen and Grossberg [

During hardware implementation, time delays do exist due to finite switching speed of the amplifiers and communication time and, thus, delays should be incorporated into the model equations of the network. For model (

Some other more detailed justifications for introducing delays into model equations of neural networks can be found in [

In addition to the delay effects, stochastic effects constitute another source of disturbances or uncertainties in real systems [

However, besides delay and stochastic effects, diffusion effect cannot be avoided in the neural networks when electrons are moving in asymmetric electromagnetic fields [

The remainder of this paper is organized as follows. In Section

For any

There exist positive constants

For each

There exist positive functions

There exists positive constant

There are nonnegative functions

There are nonnegative constants

The following inequality holds:

The trivial solution of (

Let

The following lemmas are important in our approach.

Assume there exist constants

For two positive-valued functions

Under assumptions

Consider the following Lyapunov function:

In Theorem

Under assumptions

When

Under assumptions

In Corollary

Under assumptions

Model (

When

When

In this section, a numerical example is presented to illustrate the correctness of our main result.

Consider a two-dimensional stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays as follows:

One can find that models considered in [

It is obvious that the results in [

Numerical solution

In this paper, stochastic Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion have been investigated. All features of stochastic systems (especially the connection matrices and delays are time-varying) reaction-diffusion systems have been taken into account in the neural networks. Without requiring the differential and monotonicity of the activation functions and the symmetry of the connection matrices, a set of new sufficient conditions for checking

The authors are extremely grateful to two anonymous reviewers, and particularly to Professor Yong Zhou for their valuable comments and suggestions, which have contributed a lot to the improved presentation of this paper. This work was supported in part by the National Natural Science Foundation of China under Grants no. 50925727, no. 10971240, and no. 60876022, the Foundation of Chinese Society for Electrical Engineering, the Foundation of Yunnan Provincial Education Department under Grant no. 07Y10085, the Scientific Research Fund of Yunnan Province under Grant no. 2008CD186.