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

In this paper, Cohen-Grossberg shunting inhibitory cellular neural networks(CGSICNNs) on time scales are investigated. Some sufficient conditions which ensure the existence and global exponential stability of anti-periodic solutions for a class of CGSICNNs on time scales are established. Numerical simulations are carried out to illustrate the theoretical findings. The results obtained in this paper are of great significance in designs and applications of globally stable anti-periodic Cohen-Grossberg shunting inhibitory cellular neural networks. c ©2016 All rights reserved.

[1]  R. B. Pinter,et al.  Shunting inhibitory cellular neural networks: derivation and stability analysis , 1993 .

[2]  Aiping Zhang,et al.  Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays , 2013 .

[3]  Wentao Wang,et al.  Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms , 2013, Neurocomputing.

[4]  Yang Liu,et al.  Existence and global exponential stability of almost periodic solutions to Cohen-Grossberg neural networks with distributed delays on time scales , 2014, Neurocomputing.

[5]  V. Lakshmikantham,et al.  Hybrid systems on time scales , 2002 .

[6]  Xiaodi Li,et al.  Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays , 2009, Appl. Math. Comput..

[7]  Changjin Xu,et al.  Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms , 2016 .

[8]  Changjin Xu,et al.  Existence and Exponential Stability of Anti-periodic Solutions for a High-Order Delayed Cohen–Grossberg Neural Networks with Impulsive Effects , 2013, Neural Processing Letters.

[9]  Lihong Huang,et al.  Existence and exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with bounded and unbounded delays , 2007, Comput. Math. Appl..

[10]  Shun-Tang Wu,et al.  Periodic solutions for dynamic equations on time scales , 2009 .

[11]  Wentao Wang,et al.  Anti-periodic solutions for a class of nonlinear nth-order differential equations with delays , 2009 .

[12]  Huiyan Kang,et al.  Anti-Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Continuously Distributed Delays , 2010, 2010 2nd International Conference on Information Engineering and Computer Science.

[13]  Jinde Cao,et al.  Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses , 2007 .

[14]  Peilin Shi,et al.  Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses , 2010, Appl. Math. Comput..

[15]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[16]  Yongkun Li,et al.  Existence and Stability of Antiperiodic Solution for a Class of Generalized Neural Networks with Impulses and Arbitrary Delays on Time Scales , 2010 .

[17]  Hongyong Zhao,et al.  Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients , 2008 .

[18]  Changjin Xu,et al.  Anti-periodic solutions in a ring of four neurons with multiple delays , 2015, Int. J. Comput. Math..

[19]  Jianying Shao,et al.  Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays☆ , 2008 .

[20]  Youssef N. Raffoul,et al.  Periodic solutions for a neutral nonlinear dynamical equation on a time scale , 2006 .

[21]  M. Rashford,et al.  Exponential Stability of Dynamic Equations on Time Scales , 2022 .

[22]  A. Peterson,et al.  Advances in Dynamic Equations on Time Scales , 2012 .

[23]  S. Hilger.  Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[24]  Jinde Cao,et al.  Anti-periodic solution for delayed cellular neural networks with impulsive effects , 2011 .

[25]  Chunxia Ou,et al.  Anti-periodic solutions for high-order Hopfield neural networks , 2008, Comput. Math. Appl..

[26]  Li Yang,et al.  Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays , 2009 .

[27]  Shuhua Gong,et al.  Anti-periodic solutions for a class of Cohen-Grossberg neural networks , 2009, Comput. Math. Appl..

[28]  Zuda Huang,et al.  ANTI-PERIODIC SOLUTIONS FOR HIGH-ORDER CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS , 2010 .

[29]  Maoan Han,et al.  Periodic boundary value problems of integro-differential equation of Volterra type on time scales☆ , 2008 .

[30]  Changjin Xu,et al.  Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay , 2015, Neurocomputing.

[31]  Yongkun Li,et al.  Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales , 2011 .