变时滞Cohen-Grossberg随机反应扩散神经网络的吸引集和不变集

Attracting and Invariant Sets of Stochastic Reaction-diffusion Cohen-Grossberg Neural Networks with Time-varying Delays

从M.Cohen和S.Grossberg(IEEE Trans Sys Man Cyber,1983,13:815-826.)提出Cohen-Gross-berg神经网络以来,由于它在信号和图像处理、联想记忆、组合优化等中的广泛应用,因此受到了广泛的关注和研究.由于随机干扰和反应扩散,时滞Cohen-Grossberg随机反应扩散神经网络的平衡点往往不存在,这时,往往研究其吸引集和不变集的存在性.建立了一种研究时滞Cohen-Grossberg随机反应扩散神经网络的吸引集与不变集的方法.通过应用Ito公式、时滞微分不等式技巧和M-矩阵性质,获得了判定变时滞Cohen-Grossberg随机反应扩散神经网络存在吸引集和不变集的充分条件.所获得的充分条件在实践当中可以用简单的代数方法验证,因此有广泛的应用价值.最后举例用以说明我们的结果的有效性.

Since Cohen-Grossberg neural network was first proposed by M.Cohen and S.Grossberg（IEEE Trans Syst Man Cybernet,1983,SMC-13：815-826.）,many researchers have done extensive studies on this subject due to their extensive applications in many fields such as associative memory,signal and image processing and combinatorial optimization.Because of the random perturbation and reaction-diffusion,the equilibrium point of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays sometimes does not exist.So,we should study the existence of attracting set and invariant set of it.In this paper,we establish a method to study the existence of attracting set and invariant set of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays.By using Ito formula,the properties of M-cone and inequality technique,we obtain some sufficient conditions ensuring the existence of attracting set and invariant set of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays.The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range.Examples are also given to illustrate the efficiency of the obtained results.