Global exponential stability in DCNNs with distributed delays and unbounded activations

摘要

We study delayed cellular neural networks (DCNNs) whose state variables are governed by nonlinear integrodifferential differential equations with delays distributed continuously over unbounded intervals. The networks are designed in such a way that the connection weight matrices are not necessarily symmetric, and the activation functions are globally Lipschitzian and they are not necessarily bounded, differentiable and monotonically increasing. By applying the inequality pap-1b⩽(p-1)ap+bp, where p denotes a positive integer and a,b denote nonnegative real numbers, and constructing an appropriate form of Lyapunov functionals we obtain a set of delay independent and easily verifiable sufficient conditions under which the network has a unique equilibrium which is globally exponentially stable. A few examples added with computer simulations are given to support our results.