New Results on Exponential Stability of Competitive Neural Networks with Multi‐Proportional Delays

Abstract

In this paper, we are concerned with a class of competitive neural networks with multi‐proportional delays. By applying the Banach fixed point theorem and constructing suitable Lyapunov functions, we obtain new sufficient conditions for the global exponential stability to this class of neural networks, which are easily verifiable. Finally, two examples are given to illustrate the effectiveness of the obtained results.

Almost sure stability of stochastic neutral Cohen–Grossberg neural networks with Lévy noise and time‐varying delays

“…Because of the influence for numerous complex factors in reality, which may lead to the stability or instability for the stochastic hybrid system (SHS), the stability problems of SHS have become a hot research theme [1][2][3][4][5][6][7][8][9], especially the neural networks (NNs) [10][11][12][13][14][15]. The Cohen-Grossberg neural networks (CGNNs) molding is a special type of NNs which was originally raised and researched by Cohen Grossberg in 1983 [16].…”

Existence and Global Attractivity of Pseudo Almost Periodic Solutions for Clifford-Valued Fuzzy Neural Networks with Proportional Delays

“…In [16], the finite time synchronization problem of a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays is investigated. In [17], a class of competitive neural networks with multiple proportional delays is studied, and a new sufficient condition for the global exponential stability of such a network is obtained.…”

“…They are neural networks that incorporate fuzzy logic into the structure of traditional cellular neural networks. They have important applications in image processing and pattern recognition; therefore, fuzzy neural networks have been widely studied [14][15][16][17][18][19][20][21].…”

Almost sure exponential stability of hybrid stochastic delayed Cohen–Grossberg neural networks

“…Thereupon that the stability problem of neural networks has received extensive attention and research. Nevertheless, the investigations on stability of stochastic neural networks are mainly focused on the pth moment exponential stability [12,13], the global exponential stability [14][15][16], and the robust exponential stability [17][18][19]. There is little attention paid to the almost sure exponential stability.…”