具有混合时滞的随机Cohen-Grossberg神经网络的稳定性分析

Stability Analysis of Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays

研究了均方意义下的具有时变时滞与分布时滞的随机Cohen-Grossberg神经网络的指数稳定性,利用It微分公式和Lyapunov泛函,得到了一个关于其指数稳定时滞无关的充分条件.具体实施方法是运用It微分公式沿所考虑的神经网络对构造的Lyapunov泛函进行微分,得到了系统稳定的代数判据.最后,通过一个数学样例说明了所得结论的有效性.目前文献尚未见同时具有时变时滞与分布时滞的随机Cohen-Grossberg神经网络的指数稳定性的相应结果,由于Cohen-Grossberg神经网络更具有代表性,其研究意义与应用前景不言而喻.

Mean square exponential stability of Cohen-Grossberg neural networks with timevarying delays and distributed time delays is analyzed. By using differential formula and Lyapunov functional, a new delay-independent sufficient condition for exponential stability is derived. By Ito. differential formula, the stochastic derivative of Lyapunov functional along the considered neural network is obtained. Finally, a numerical example is given to demonstrate the usefulness of the proposed stability criteria. To the best of our knowledge, there are few results about the mean square exponential stability analysis of Cohen-Grossberg neural networks with time-varying delays and distributed time delays. Due to the representation of Cohen-Grossberg neural networks, it is significant to study its exponential stability.