Almost periodic solutions for SICNNs with time-varying delays in the leakage terms

This paper is concerned with the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays in the leakage (or forgetting) terms. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of almost periodic solutions by using Lyapunov functional method and differential inequality techniques. We also provide numerical simulations to support the theoretical result.

[1]  Zhibin Chen A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type , 2012, Neural Computing and Applications.

[2]  Christof Koch,et al.  Visual Information Processing: From Neurons to Chips , 1991 .

[3]  Toshiki Naito,et al.  Functional Differential Equations With Infinite Delay , 1991 .

[4]  Xianguo Geng,et al.  A new Neumann type integrable system related to the coupled Harry–Dym hierarchy , 2005 .

[5]  M. L. Cartwright,et al.  Almost periodic differential equations and almost periodic flows , 1969 .

[6]  Changhong Zhao,et al.  Anti-Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Time-Varying Coefficients , 2010, Neural Processing Letters.

[7]  Hong Zhang,et al.  Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms , 2013, Appl. Math. Comput..

[8]  Jinde Cao,et al.  Almost periodic attractor of delayed neural networks with variable coefficients , 2005 .

[9]  Shigeo Abe,et al.  Neural Networks and Fuzzy Systems , 1996, Springer US.

[10]  Rudolf Kruse,et al.  of Neural Networks , 2008 .

[11]  Jinde Cao,et al.  Almost periodic solution of shunting inhibitory CNNs with delays , 2002 .

[12]  Zhaohui Yuan,et al.  Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays , 2008, Math. Comput. Simul..

[13]  K. Gopalsamy Leakage delays in BAM , 2007 .

[14]  Bahram Nabet,et al.  Analysis and analog implementation of directionally sensitive shunting inhibitory neural networks , 1991, Defense, Security, and Sensing.

[15]  A. Fink Almost Periodic Differential Equations , 1974 .

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

[17]  Mingquan Yang,et al.  Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays , 2013 .

[18]  Jinde Cao,et al.  Delay-dependent stability of neural networks of neutral type with time delay in the leakage term , 2010 .

[19]  Pagavathigounder Balasubramaniam,et al.  Leakage Delays in T–S Fuzzy Cellular Neural Networks , 2011, Neural Processing Letters.

[20]  Simon Haykin,et al.  Neural networks , 1994 .

[21]  Bingwen Liu Global exponential stability for BAM neural networks with time-varying delays in the leakage terms☆ , 2013 .

[22]  F. Yi Global Asymptotic Stability of Neutral Neural Networks with Time Delay , 2010 .

[23]  Pagavathigounder Balasubramaniam,et al.  Asymptotic stability of BAM neural networks of neutral-type with impulsive effects and time delay in the leakage term , 2011, Int. J. Comput. Math..

[24]  Jinde Cao,et al.  Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay , 2003 .

[25]  K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[26]  Xiaodi Li,et al.  Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations , 2011, J. Frankl. Inst..

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

[28]  Qiyi Fan,et al.  Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying and continuously distributed delays , 2010 .