Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales

Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales

“…Many authors have investigated the dynamical behaviors of neural networks on time scales. For instance, in [37][38][39], authors studied periodic solutions to some BAM neural networks on time scales; in [40,41], authors studied almost periodic solutions of some neural networks on time scales; in [42], authors studied anti-periodic solutions of a class of shunting inhibitory cellular neural networks with impulses on time scales.…”

Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms

“…We know that the existence and stability of anti-periodic solutions play a key role in characterizing the behavior of nonlinear differential equations [3,4,10,14,18,19,20,22,23,24,26,27,31,32,35,36]. For example, the signal transmission process of neural networks can often be described as an anti-periodic process.…”

“…In recent years, the anti-periodic problems of neural networks have been investigated by numerous scholars [3,4,10,18,19,20,22,23,24,26,31,35]. Considering that a typical time delay called Leakage (or "forgetting") delay may exist in the negative feedback term of the neural networks system (these terms are variously known as forgetting or leakage terms), some authors discussed the anti-periodic solution of neural networks with delays in the leakage terms (see [5,6,8,12,14,20,24,27,36]). Very recently, another type of time-delays, namely, neutral-type time-delays which always appears in the study of automatic control, population dynamics and vibrating masses attached to an elastic bar, etc., has recently drawn considerable attention [16].…”

Anti-periodic solutions of Cohen-Grossberg shunting inhibitory cellular neural networks on time scales

“…Thus the existence and stability of anti-periodic solutions are an important topic in characterizing the behavior of nonlinear differential equations [7,8,10,15,16,17,18,21,22,23,24,25,26,29,30,31,32,33,34]. Therefore it is worth while to investigate the existence and stability of anti-periodic solutions for BAM neural networks.…”