Existence and Stability of Antiperiodic Solution for a Class of Generalized Neural Networks with Impulses and Arbitrary Delays on Time Scales

Abstract

By using coincidence degree theory and Lyapunov functions, we study the existence and global exponential stability of antiperiodic solutions for a class of generalized neural networks with impulses and arbitrary delays on time scales. Some completely new sufficient conditions are established. Finally, an example is given to illustrate our results. These results are of great significance in designs and applications of globally stable anti-periodic Cohen-Grossberg neural networks with delays and impulses .

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

“…Arising from problems in applied sciences, it is well-known that the existence of anti-periodic solutions plays a key role in characterizing the behavior of nonlinear differential equations as a special periodic solution and have been extensively studied by many authors during the past ten years, see [10][11][12][13][14] and references therein. For example, anti-periodic trigonometric polynomials are important in the study of interpolation problems [30], and anti-periodic wavelets are discussed in [31].…”

“…In contrast, however, very few results are available on the existence and exponential stability of anti-periodic solutions for neural networks, while the existence of anti-periodic solutions plays a key role in characterizing the behavior of nonlinear differential equations (see [10][11][12][13][14]). Since SICNNs can be analog voltage transmission, and voltage transmission process often a anti-periodic process.…”

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.…”

“…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]).…”

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.…”