不连续激励函数时滞Cohen-Grossberg神经网络的动力学性质(英文)

Regular dynamics in delayed Cohen-Grossberg neural networks with discontinuous activation functions

研究了一类具有不连续激励函数的时滞Cohen-Grossbe神经网络,利用推广的Lyapunov方法,证明了Filippov意义下解全局收敛到惟一的平衡点.在证明过程中使用了链式法.利用该法则可以计算不可微Lyapunov函数对时间t沿右端不连续微分方程的导数.

A class of Cohen-Grossberg neural networks where the neuron activations are modeled by discontinuous functions was considered. A tool, the chain rule for computing the time derivative along the neural network solutions of a nondifferentiable Lyapunov function, is used which enables us to apply a Lyapunov-like approach to differential equations with discontinuous right-hand side. By means of the Lyapunov-like approach, a general result is proved on global exponential convergence toward a unique equilibrium point of the neural network solutions in the sense of Filippov.