1 - 8 of 8 Chapters
[The dynamics of artificial neural networks is one of the most applicable and attractive objects for the mathematical foundations of neuroscience. In the last decades, recurrent neural networks (RNNs), Cohen–Grossberg neural networks (Hopfield neural networks as a special version), and cellular...
[Differential equations with piecewise constant argument (EPCA) were proposed for investigations in [63, 91] by founders of the theory, K. Cook, S. Busenberg, J. Wiener, and S. Shah. They are named as differential EPCA. In the last three decades, many interesting results have been obtained, and...
[In this chapter we consider Hopfield-type neural networks systems with piecewise constant argument of generalized type. Sufficient conditions for the existence of a unique equilibrium and a periodic solution are obtained. The stability of these solutions is investigated.]
[In this chapter we introduce two different types of impulsive neural networks with piecewise constant argument of generalized type called (θ, θ)−type neural networks and (θ, τ)−type neural networks, respectively. For these types, sufficient conditions for existence of a unique equilibrium are...
[In this chapter we derive some sufficient conditions for the existence and stability of periodic solutions for each (θ, θ)-type neural networks and (θ, τ)-type neural networks, respectively. Examples with numerical simulations are given to illustrate our results.]
[In this chapter, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of RNNs. The model involves alternating argument. Sufficient conditions are obtained for global exponential stability of the equilibrium point....
[In this chapter, by using the concept of differential equations with piecewise constant arguments of generalized type [13–15, 18], the model of cellular neural networks (CNNs) [79, 80] is developed. Lyapunov–Razumikhin technique is applied to find sufficient conditions for uniform asymptotic...
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