Periodicity and stability analysis of impulsive neural network models with generalized piecewise constant delays

Abstract

In this paper, the global exponential stability and periodicity are investigated for impulsive neural network models with Lipschitz continuous activation functions and generalized piecewise constant delay. The sufficient conditions for the existence and uniqueness of periodic solutions of the model are established by applying fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of impulsive neural network models with variable and/or deviating arguments. The results extend some previous results. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion.

Stability Analysis of Periodic Solutions in Alternately Advanced and Retarded Neural Network Models with Impulses

“…Based on the proposed approach, it is unnecessary to utilize Razumikhin-type technique or construct a Lyapunov function that is applied from the previous literature. Moreover, illustrative simulation examples show that the approach used is more efficient and extend the results of the previous literature [1,10,14,17].…”

“…When the the impulsive effects are absent, the stability result of Corollary 3.28 reduces to the stability result of [17,Theorem 3] with generalized piecewise alternately advanced and retarded argument and Corollary 3.30 reduces to the results of [15,Theorem 5.1] with generalized piecewise constant delay. We are able to see that the results obtained in this article extend and improve the results given in [1,2,10,14,15,17].…”

“…(i) The ICNN models with the IDEGPCD system (the respective constant coefficients) is neither more nor less than system (1.1) in [1]. Since those works not have a global IDEGPCD's Gronwall-type inequality, the results for this system have more stronger conditions, see [ (iii) The condition (E) with κ − < 1 and γ k = t k , k ∈ N, reduces to the condition (E ) which is the same condition (E) in [14].…”

“…From this point, the model considered in this paper is more general than the existing the ICNN models and the CNN models with piecewise constant argument such as those in References [1,2,10,14,15,17].…”

“…(4) In [14] (2021), sufficient conditions for the periodic solution of the IDEGPCD system are established.…”