New Stability Criteria for High-Order Neural Networks with Proportional Delays*
Changjin Xu, Pei-Luan Li · Communications in Theoretical Physics · 2017
Abstract This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation y i ( t ) = u i ( e t ) ( i = 1 , 2 , … , n ) , we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and time-varying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.