An anti-periodic solution for a class of recurrent neural networks

Abstract

a b s t r a c tIn this paper recurrent neural networks with time-varying delays and continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the anti-periodic solutions are established, which are new and complement previously known results.

The existence and stability of the anti-periodic solution for delayed Cohen–Grossberg neural networks with impulsive effects

“…It is known that CGNNs model (1) includes some well-known neural networks such as Hopfield neural networks, cellular neural networks and recurrent neural networks as a special case. From this point, we can conclude that our results are more practical than those in [13][14][15].…”

“…One can observe that all the results in [13][14][15][16] and the references therein cannot be applicable to system (28) to obtain the existence and exponential stability of the anti-periodic solutions. This implies that the results of this paper are essentially new.…”

“…For details, see [13][14][15]18] and references therein. In [13], the author considered the existence and exponential stability of the anti-periodic solutions for a class of recurrent neural networks with time-varying delays and continuously distributed delays. In [14], by constructing fundamental function sequences based on the solution of networks, the authors studied the existence of anti-periodic solutions for Hopfield neural networks with impulses.…”

Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen-Grossberge neural networks on time scales

“…Arising from problems in applied sciences, the existence of anti-periodic solutions plays a key role in characterizing the behavior of nonlinear differential equations (see [25][26][27][28][29]). It is worth continuing the investigation of the existence and stability of anti-periodic solutions of impulsive fuzzy Cohen-Grossberg neural networks.…”

Anti-periodic solutions for a class of second order differential equations

“…Recently, anti-periodic problems have been extensively studied by many authors. For example, anti-periodic problems of Rayleigh-type equation have been discussed in [1,5,9], existence of solution for anti-periodic boundary conditions have been studied in [4,8], and anti-periodic problems of neural networks have already been considered in [2,3,7].…”