Anti-Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Time-Varying Coefficients

Abstract

This paper is concerned with the existence and exponential stability of anti-periodic solutions for shunting inhibitory cellular neural networks (SICNNs) with timevarying coefficients arising from the description of the neurons' state in delayed neural networks. Some new sufficient conditions ensuring the existence and exponential stability of anti-periodic solutions for SICNNs are established.

Weighted Pseudo Anti‐Periodic Solutions for Cellular Neural Networks with Mixed Delays

“…Since the existence and exponential stability of weighted pseudo anti-periodic solutions for cellular neural networks with mixed delays has not been studied before, it is clearly to see that all results obtained in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] are invalid for example (1.1) with (2.12). Here a novel proof is employed to establish some criteria which guarantee the global exponential stability of weighted pseudo anti-periodic solutions for cellular neural networks with mixed delays.…”

Almost automorphic solutions for shunting inhibitory cellular neural networks with time-varying delays

“…In this paper, we consider the almost automorphic solutions of ( 1 ), which complement with some previous studies in (Shao 2008 ; Peng and Huang 2009 ; Zhao et al. 2010 ; Peng and Wang 2013 ; Zhou et al. 2006a ; Zhao and Zhang 2008 ; Cai et al.…”

“…Peng and Huang ( 2009 ) investigated the existence and exponential stability of anti-periodic solutions for model ( 1 ) with and Zhao et al. ( 2010 ) considered anti-periodic solutions of model ( 1 ) with the and . Peng and Wang (2011) analyzed the anti-periodic solutions for ( 1 ) with time-varying delays in leakage terms.…”

Global Exponential Stability of Pseudo Almost Periodic Solutions for SICNNs with Time-Varying Leakage Delays

“…In particular, there have been extensive results on the problem of the existence and stability of the equilibrium point and periodic and almost periodic solutions of SICNNs with time-varying delays in the literature. We refer the reader to [1][2][3][4][5][6][7] and the references cited therein.…”

“…Then, [19,20], the authors obtained the existence of almost periodic solution of SICNNs with leakage delays, but they did not give the existence and global exponential convergence for the pseudo almost periodic solution. Since [1][2][3][4][5][6][7][8][9] only dealt with SICNNs without leakage delays, [14][15][16][17][18][21][22][23][24] give no opinions about the problem of pseudo almost periodic solutions for SICNNs with leakage delays. One can observe that all the results in these literatures and the references therein cannot be applicable to prove the existence and exponential stability of pseudo almost periodic solutions for SICNNs (56).…”