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In this paper, we address a new model of neural networks related to the impulsive phenomena which is called state-dependent impulsive recurrent neural networks with time-varying and continuously distributed delays. We investigate sufficient conditions on the existence and uniqueness of exponentially stable anti-periodic solution for these neural networks by employing method of coincide degree theory and an appropriate Lyapunov function. Moreover, we present an illustrative example to show the effectiveness and feasibility of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we give a detailed Hopf bifurcation analysis of a recurrent neural network system involving both discrete and distributed delays. Choosing the sum of the discrete delay terms as a bifurcation parameter the existence of Hopf bifurcation is demonstrated. In particular, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are studied by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. [ABSTRACT FROM AUTHOR]

In this paper, chaotification of delayed recurrent neural networks via chaotically changing moments of impulsive actions is considered. Sufficient conditions for the presence of Li-Yorke chaos with its ingredients proximality, frequent separation, and existence of infinitely many periodic solutions are theoretically proved. Finally, effectiveness of our theoretical results is illustrated by an example with numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a more general class of state-dependent impulsive Cohen–Grossberg neural networks having variable coefficients with time-varying delays is addressed. By means of B -equivalence method, we reduce this state-dependent impulsive neural networks system to a fix time impulsive neural networks system. Sufficient conditions for existence and global exponential stability of the equilibrium point as well as periodic solution are obtained by employing a suitable Lyapunov function, the Banach fixed point theorem and the Halanay-type impulsive differential inequality technique. Finally, two examples with numerical simulations to show the effectiveness of our theoretical results are illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we consider existence and global exponential stability of periodic solution for state-dependent impulsive shunting inhibitory cellular neural networks with time-varying delays. By means of B -equivalence method, we reduce these state-dependent impulsive neural networks system to an equivalent fix time impulsive neural networks system. Further, by using Mawhin’s continuation theorem of coincide degree theory and employing a suitable Lyapunov function some new sufficient conditions for existence and global exponential stability of periodic solution are obtained. Previous results are improved and extended. Finally, we give an illustrative example with numerical simulations to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the global robust asymptotic stability of the equilibrium point for a more general class of bidirectional associative memory (BAM) neural networks with variable time of impulses is addressed. Unlike most existing studies, the case of non-fix time impulses is focused on in the present study. By means of B -equivalence method, which was introduced in Akhmet (2003, 2005, 2009, 2010), Akhmet and Perestyuk (1990) and Akhmet and Turan (2009), we reduce these networks to a fix time impulsive neural networks system. Sufficient conditions ensuring the existence, uniqueness and global robust asymptotic stability of the equilibrium point are obtained by employing an appropriate Lyapunov function and linear matrix inequality (LMI). Finally, we give one illustrative example to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]