Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones.

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

[2]  Qiyuan Zhou,et al.  Exponential convergence of shunting inhibitory cellular neural networks with continuously distributed delays , 2010 .

[3]  Lin Wang,et al.  Stability of Cohen-Grossberg neural networks with distributed delays , 2005, Appl. Math. Comput..

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

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

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

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

[8]  Yuehua Yu,et al.  Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays , 2007 .

[9]  Ju H. Park,et al.  Further result on asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays , 2006, Appl. Math. Comput..

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

[11]  Changming Ding,et al.  Synchronization of stochastic perturbed chaotic neural networks with mixed delays , 2010, J. Frankl. Inst..

[12]  O. M. Kwona,et al.  Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays , 2008 .

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

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

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

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

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

[18]  Neil Genzlinger A. and Q , 2006 .

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

[20]  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..

[21]  Zhibin Chen,et al.  Exponential convergence for HRNNs with continuously distributed delays in the leakage terms , 2012, Neural Computing and Applications.

[22]  Lihong Huang,et al.  Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays , 2006 .