Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Abstract

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of -matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

Robust Exponential Stability of Switched Complex‐Valued Neural Networks with Interval Parameter Uncertainties and Impulses

“…Activation functions in complex number domains that satisfy Assumption 1 are actually the extensions of the real-valued functions that satisfy the Lipschitz continuity condition. As demonstrated in [2,7,14,34,35], it is easy to verify that assumptions concerning the conditions of the decomposition of a complex-valued activation function into its real and imaginary parts in [8,10,13] are strong constraints, and that, in this case, shows a special case of Assumption 1. In order to unify the research approach using real-valued systems and complex-valued systems, it is assumed that complex-valued activation functions are not explicitly expressed by separating real and imaginary parts, but by satisfying the Lipschitz continuity condition.…”

Mean Square Exponential Stability of Stochastic Complex‐Valued Neural Networks with Mixed Delays

“…Therefore, the more appropriate way is to incorporate continuously distributed delays [3][4][5][6][7]. In [8][9][10][11], the authors have studied several kinds of complex-valued neural networks with continuously distributed delays. Some significant results were obtained for assuring the stability of the proposed systems in [8][9][10][11].…”

“…In fact, most real models of neural networks are affected by many external and internal perturbations which are of great uncertainty, such as impulsive disturbances [5,[9][10][11][12][13][14][15], Markovian jumping parameters [16][17][18][19], and parameter uncertainties [20][21][22]. As Haykin [23] points out, in real nervous systems, synaptic transmission is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes.…”

Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

“…In application's point of view, a fundamental problem of applying neural networks is stability. This is a prerequisite for ensuring that the developed networks can work normally [7][8][9][10]. Thus, a popular topic about the stability analysis and stabilization of SNNs has been considered in [11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”