On Antiperiodic Solutions for Cohen-Grossberg Shunting Inhibitory Neural Networks with Time-Varying Delays and Impulses

Abstract

In this letter, a class of Cohen-Grossberg shunting inhibitory neural networks with time-varying delays and impulses is investigated. Sufficient conditions for the existence and exponential stability of antiperiodic solutions of such a class of neural networks are established. Our results are new and complementary to previously known results. An example is given to illustrate the feasibility and effectiveness of our main results.

Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks

“…which is of the form jg T (z)j( )jg(z)j 0 or equivalently jg T (z)j jg(z)j 0: On the other hand, if is a positive de…nite matrix, then, for all g(z(t)) 6 = 0, we have jg T (z)j jg(z)j > 0: Obviously, when > 0, (14) contradicts with (15), implying that under the condition of Theorem 1, the equilibrium equation of system (5) given by (6) cannot have a solution where g(z) 6 = 0. Thus, we can conclude that Theorem 1 guarantees that the origin of system (5) is the unique equilibrium point.…”

Effect of Proportional Delays and Continuously Distributed Leakage Delays on Global Exponential Convergence of CNNS

“… focused on the problem of stabilization of sampled‐data neural‐ network‐based systems with state quantization. For more related works on these aspects, we refer the readers to and the references cited therein.…”

“…For example, Xu et al [3] studied the exponential stability of almost periodic solutions for memristor-based neural networks with distributed leakage delays, Balasubramaniam et al [4] investigated the existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays, Balasubramaniam Manuscript et al [5] discussed the global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays, Wang et al [39] focused on the problem of stabilization of sampled-data neuralnetwork-based systems with state quantization. For more related works on these aspects, we refer the readers to [6][7][8][9][21][22][23][24][25][36][37][38][41][42][43] and the references cited therein.…”

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.…”