New Stability Criteria for High-Order Neural Networks with Proportional Delays

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 yi（t） = ui（ et）（i = 1, 2,..., n）, w...

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Bibliographic Details
Published inCommunications in theoretical physics Vol. 67; no. 3; pp. 235 - 240
Main Author 徐昌进 李培峦
Format Journal Article
LanguageEnglish
Published 01.03.2017
Subjects
Brouwer不动点定理
全局指数稳定性
微分不等式
无界时滞
比例
稳定性判据
非线性变换
高阶神经网络
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ISSN0253-6102
DOI10.1088/0253-6102/67/3/235

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Summary: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 yi（t） = ui（ et）（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 timevarying 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.
Bibliography: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 yi（t） = ui（ et）（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 timevarying 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.
Chang-Jin Xu1 ,Pei-Luan Li2 （ 1Cuizhou Key Laboratory of Economics System Simulation, Cuizhou University of Finance and Economics, Guiyang 550004, China ;2School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China）
11-2592/O3
high-order neural networks, exponential stability, proportional delays, delay differential inequality, Brouwer fixed point theorem
ISSN:0253-6102
DOI:10.1088/0253-6102/67/3/235