Global exponential stability of Hopfield neural networks with distributed delays

Abstract

In this paper, dynamical behaviors of Hopfield neural networks system with distributed delays were studied. By using contraction mapping principle and differential inequality technique, a sufficient condition was obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model. Here we point out that our methods, which are different from previous known results, base on the contraction mapping principle and inequality technique. Two remarks were also worked out to demonstrate the advantage of our results.

Global Exponential Stability of High-Order Neural Networks with Time-Varying Coefficients and Delays

“…To the best of our knowledge, there are few results about this problems. Here, we point out that our approach, which is different from previously known results, based on the analytical techniques and differential inequality techniques [18,19].…”

“…In recent years, the neural networks characterized by firstorder equations have been extensively investigated and various sufficient stability conditions have been proposed for such neural networks(see, e.g., [14][15][16][17][18][19]). However, the performances of such neural network models are shown to have limitations such as limited capacity when used in pattern recognition problems and optimization problems.…”

Exponential Stability of Stochastic Differential Equation with Mixed Delay

“…An improved delay-dependent stability criterion is derived for stochastic delay systems by a strict LMI in [14]. Hu and Wu [15], Wu et al [16], Yin et al [17], and Zhou et al [18] established some stability criteria of the stochastic system with distributed delays. However, discrete delays and distributed delays always coexist in real dynamic systems; thus, it is reasonable to consider them together and it leads us to investigate stochastic differential equations with mixed delays (SMDDEs for short).…”

Long Time Behavior for a System of Differential Equations with Non-Lipschitzian Nonlinearities

“…The literature is very rich of works on the asymptotic behavior of solutions for special cases of system (1) (see for instance [10][11][12][13][14][15][16][17][18][19]). Here the integral terms represent some kind of distributed delays but discrete delays may be recovered as well by considering delta Dirac distributions.…”