Impulsive Hopfield-type neural network system with piecewise constant argument (original) (raw)

Exponential stability of Hopfield neural networks with time-varying delays via impulsive control

Mathematical Methods in the Applied Sciences, 2010

In this paper, by utilizing the Lyapunov functionals, the analysis method and the impulsive control, we analyze the exponential stability of Hopfield neural networks with time-varying delays. A new criterion on the exponential stabilization by impulses and the exponential stabilization by periodic impulses is gained. We can see that impulses do contribution to the system's exponential stability. Two examples are given to illustrate the effectiveness of our result.

Almost periodic solutions of impulsive neural networks at non-prescribed moments of time

Neurocomputing, 2014

In this paper, we address a new model of neural networks related to the discontinuity phenomena which is called impulsive recurrent neural networks with variable moments of time. Sufficient conditions for existence and uniqueness of exponentially stable almost periodic solution are investigated. An example is given to illustrate our theoretical results.

Almost periodic solutions of impulsive integro‐differential neural networks*

Mathematical Modelling and Analysis, 2010

In this paper, sufficient conditions are established for the existence of almost periodic solutions for system of impulsive integro‐differential neural networks. Our approach is based on the estimation of the Cauchy matrix of linear impulsive differential equations. We shall employ the contraction mapping principle as well as Gronwall‐Bellman's inequality to prove our main result. The research of Gani Tr. Stamov is partially supported by the Grand 100ni087–16 from Technical University–Sofia

Stability and Hopf-Bifurcating Periodic Solution for Delayed Hopfield Neural Networks with n Neuron

Journal of Applied Mathematics, 2014

We consider a system of delay differential equations which represents the general model of a Hopfield neural networks type. We construct some new sufficient conditions for local asymptotic stability about the trivial equilibrium based on the connection weights and delays of the neural system. We also investigate the occurrence of an Andronov-Hopf bifurcation about the trivial equilibrium. Finally, the simulating results demonstrate the validity and feasibility of our theoretical results.

Stability analysis of neural networks with periodic coefficients and piecewise constant arguments

Global exponential stability of a class of neural networks with periodic coefficients and piecewise constant arguments is investigated in this paper. A new definition of exponential stability and a novel differential inequality with piecewise constant arguments are introduced to obtain sufficient conditions for the globally exponential stability of the periodic solution of neural networks. The stability criteria are independent on the upper bound of the adjacent element difference of the discontinuous switching moments. According to the new definition of exponential stability and the novel differential inequality, not only it is not necessary to establish any relationship between the norms of the states with/without piecewise constant arguments, but also the stability criteria for the neural networks can be obtained just in terms of the original differential equation, rather than the equivalent integral equation which is widely used in the early works. Typical numerical examples are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. (D. Cao).

Stability analysis of a class of general periodic neural networks with delays and impulses

International journal of neural systems, 2009

Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic neural networks with delays and impulses is studied. Some sufficient conditions are established for the existence and globally exponential stability of a unique periodic solution. Furthermore, the results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.