Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays

Global asymptotic stability of nonautonomous Cohen–Grossberg neural network models with infinite delays

“…In [14], the authors studied the global asymptotic stability of the following recurrent neural network model then the system (4.11) is globally asymptotically stable.…”

“…In [14], the authors assumed a different set of hypotheses, also including that c i (t), a ijp (t), and I i (t) are bounded functions, to get the global asymptotic stability of (4.11), since a different norm in R n was considered. (4.14) where λ j , λ i are positive constants.…”

“…In 1989, Marcus and Westervelt [18] introduced for the first time a discrete delay in the Hopfield model (1.2), and they observed that the delay can destabilize the system. In fact, the delays can affect the dynamic behavior of neural network models [1] and, for this reason, stability of delayed neural networks has been investigated extensively ( [2,3,7,8,13,14,16,19,20,23,25], and the references therein). Another relevant fact to take into account is that the neuron charging time, the interconnection weights, and the external inputs often change as time proceeds.…”

“…In Section 3, we present the results on global asymptotic stability of a general nonautonomous Cohen-Grossberg neural network model with infinite delays, which includes most of neural network models. It is important to note that most studies use a type of Lyapunov functional to obtain results on global attractivity (see [4,5,14,16,24,25]). Instead, here we use the techniques described in the work of Oliveira [20], rather than a Lyapunov functional approach.…”

“…Other authors study the global exponential stability of the models but, in these cases, they assume that the coefficients are bounded functions (see [4,23,24], and the references therein). Studies about global asymptotic stability of nonautonomous neural network models are few and the authors always assume bounded time-varying coefficients (see [14,16,22,25]). This paper aims at the global asymptotic stability of a general nonautonomous Cohen-Grossberg neural network model without assuming the existence of an equilibrium point or bounded time-varying coefficients.…”