Equilibrium analysis of delayed CNNs

Novel global asymptotic stability criteria for delayed cellular neural networks

“…The following assumption will be made throughout the paper. Assumption 1: [6] The activation function is nondecreasing, bounded and globally Lipschitz; that is (2) Then, by [6], it can be seen that there exists an equilibrium for (1). For the sake of simplicity in the stability analysis of (1), we make the following transformation to (1): (3) where is an equilibrium point of system (1).…”

“…Therefore, many researchers have investigated the problem of stability analysis for neural networks with time delays. For example, the global asymptotic stability of delayed CNNs with bounded and nonmonotonic activation functions were studied in [2] and [5], respectively, where several sufficient conditions were given via different approaches. These results were extended to a more general class of CNNs with delays in [6], [18].…”

Existence and stability of periodic solution of impulsive neural systems with complex deviating arguments

“…is an ω-periodic solution of system (1). In what follows, we apply the Halanay-type inequalities to explore sufficient conditions to ensure the global exponential stability of periodic solution.…”

“…In Section 2, we introduce some definitions and preliminary results. In Section 3, we deal with the existence of periodic solutions of system (1) by means of the continuation theorem of coincidence degree theory. Section 4 is dedicated to sufficient conditions of the global exponential stability of periodic solutions of system (1) by using the Halanay-type inequalities.…”

Global stability analysis of bidirectional associative memory neural networks with time delay

“…Van Den Driessche and Zou [17] studied the global attractivity in delayed Hopÿeld neural networks with bounded and non-monotonic activation functions. Arik and Tavsanoglu [18] studied the global stability of cellular neural networks with bounded and non-monotonic activation functions. This is practical motivation for relaxing conditions (H1) and (H2) to Assumption (A) below.…”