Abstract
We consider fuzzy shunting inhibitory cellular neural networks (FSICNNs) with time-varying coefficients and constant delays. By virtue of continuation theorem of coincidence degree theory and Cauchy–Schwartz inequality, we prove the existence of periodic solutions for FSICNNs. Furthermore, by employing a suitable Lyapunov functional we establish sufficient criteria which ensure global exponential stability of the periodic solutions. Numerical simulations that support the theoretical discussions are depicted.
Highlights
Introduction and preliminariesIn the past three decades, the cellular neural networks (CNNs) have gained a lot of popularity due to their local inter-connectivity and practical hardware implementation [1,2,3,4,5,6,7,8]
Along with pattern recognition and image processing, fuzzy cellular neural networks (FCNNs) play an essential role in cognitive science since human cognition involve many uncertainties
The dynamics of FCNNs have been widely studied by many researchers
Summary
We prove the local existence and uniqueness of solutions to (1)–(2) by means of Banach fixed point theorem To this end, set a = maxi,j aij, δ = maxi,j(. By virtue of Ascoli–Arzela lemma one can show that BV(O) and NA(I – B)V(O) are relatively compact for an open and bounded O subset of X It follows that for any open and bounded set. By means of the condition (A3), and Lemma 1.2 we get the following inequality: aij +. The operator equation U x = Vx has at least one solution in Dom U ∩ O which in turn implies that the network (1) has ω-periodic solution
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