具不连续激励函数Cohen-Grossberg神经网络周期解的全局指数稳定性

Global Exponential Stability of Periodic Solution of Delayed Cohen-Grossberg Neural Networks with Discontinuous Neuron Activations

本文研究了具时滞和周期系数的Cohen—Grossberg神经网络的稳定性.网络中的神经激励是一个可以具有跳跃间断点的单调不减函数,用来刻画神经元放大器的增益很高和趋向于无穷大的理想情形.在假设联结矩阵满足适当的条件下,我们获得了周期解存在,惟一和全局指数稳定的充分条件,且与时滞无关.所利用的假设条件与M-矩阵理论有关,容易验证.此外,由于激励函数的不连续性,我们介绍了一个适当的极限记号来研究时滞神经网络输出的收敛性.我们的结论推广了相关文献的结果.并给出了实例说明和数值模拟.

This paper is concerned with the existence and global exponential stability of periodic solutions for a nonlinear periodic system,arising from the description of the states of neurons in delayed Cohen-Grossberg type. We consider non-decreasing activations which may also have jump discontinuities in order to model the ideal situation where the gain of the neuron amplifiers is very high and tends to infinity. Under suitable assumptions on the interconnection matrices, we deduce some sufficient conditions ensuring existence as well as global exponential stability of periodic solution, the presented condition concerns the theory of M-matrices and is easy to check. Furthermore, due to the possible discontinuities of the activations functions, we introduce a suitable notation of limit to study the convergence of the output of the delayed neural networks.an numerical example are given to illustrate the theoretical results.