Abstract
Discrete neural models are of great importance in numerical simulations and practical implementations. In the current paper, a discrete model of continuous-time neural networks with variable and distributed delays is investigated. By Lyapunov stability theory and techniques such as linear matrix inequalities, sufficient conditions guaranteeing the existence and global exponential stability of the unique equilibrium point are obtained. Introduction of LMIs enables one to take into consideration the sign of connection weights. To show the effectiveness of the method, an illustrative example, along with numerical simulation, is presented.
Highlights
During the past decades, various types of neural networks have been proposed and investigated intensively, since they play important roles and have found successful applications in fields such as pattern recognition, signal and image processing, nonlinear optimization problems, and parallel computation
The dynamics of discrete-time neural networks could be quite different from those of continuous versions and will display much more complicated behaviors. It is of great theoretical and practical significance to study the dynamics of discrete neural models
Where C∗ = λ−m1(P)[λM(P) + δ1L(kM − km + 1 + δ2)]. This implies that the equilibrium solution x = 0 of system (1) is globally exponentially stable
Summary
Various types of neural networks have been proposed and investigated intensively, since they play important roles and have found successful applications in fields such as pattern recognition, signal and image processing, nonlinear optimization problems, and parallel computation. Discrete, time-varying, and distributed delays have been, respectively, introduced to describe the dynamics of neural networks, and various sufficient conditions ensuring the stability have been given. The dynamics of discrete-time neural networks could be quite different from those of continuous versions and will display much more complicated behaviors. It is of great theoretical and practical significance to study the dynamics of discrete neural models. For discrete models, such as discrete Hopfield, bidirectional associate memory, and Cohen-Grossberg neural networks, several authors [1, 7–22] have studied the existence and exponential stability of equilibria and periodic solutions. That will ignore the differences between neuronal excitatory and inhibitory effects
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