Pseudo Almost Periodic Solutions for High-Order Hopfield Neural Networks with Time-Varying Leakage Delays

In this paper, high-order Hopfield neural networks with time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. Some simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies.

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

[2]  S. Mohamad,et al.  Exponential stability in Hopfield-type neural networks with impulses , 2007 .

[3]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..

[4]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

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

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

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

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

[9]  Daoyi Xu,et al.  Impulsive delay differential inequality and stability of neural networks , 2005 .

[10]  Ravi P. Agarwal,et al.  Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations , 2010 .

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

[12]  Marat Akhmet.  On the General Problem of Stability for Impulsive Differential Equations , 2003 .

[13]  Da-Bin Wang,et al.  Three positive solutions for -Laplacian functional dynamic equations on time scales. , 2007 .

[14]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[15]  E. A. Dads,et al.  Pseudo almost periodic solutions for equation with piecewise constant argument , 2010 .

[16]  Qinghua Zhou.  Global exponential stability of BAM neural networks with distributed delays and impulses , 2009 .

[17]  Lihong Huang,et al.  Existence and exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with time-varying delays , 2007 .

[18]  Claudio Cuevas,et al.  Almost periodic and pseudo-almost periodic solutions to fractional differential and integro-differential equations , 2011, Appl. Math. Comput..

[19]  Bingwen Liu,et al.  Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays , 2015, Neurocomputing.

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

[21]  A. Alvino,et al.  On Dirichlet problem for second order elliptic equations , 1990 .

[22]  Ani Jiang.  Pseudo almost periodic solutions for a model of hematopoiesis with an oscillating circulation loss rate , 2016 .

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

[24]  Jian-an Fang,et al.  Global stability of stochastic high-order neural networks with discrete and distributed delays , 2008 .

[25]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

[26]  E. Hernández,et al.  Pseudo-almost periodic solutions for non-autonomous neutral differential equations with unbounded delay , 2008 .

[27]  Wanmin Xiong,et al.  New results on positive pseudo-almost periodic solutions for a delayed Nicholson’s blowflies model , 2016 .

[28]  Junxia Meng,et al.  Global Exponential Stability of Positive Pseudo-Almost-Periodic Solutions for a Model of Hematopoiesis , 2013 .

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

[30]  B. Xiao,et al.  Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks , 2009 .

[31]  Fuxing Zhang,et al.  ALMOST PERIODIC SOLUTIONS FOR HIGHER-ORDER HOPFIELD NEURAL NETWORKS WITHOUT BOUNDED ACTIVATION FUNCTIONS , 2007 .

[32]  Manuel Pinto,et al.  Pseudo-almost periodic solutions of neutral integral and differential equations with applications , 2010 .

[33]  Khalil Ezzinbi,et al.  Weighted pseudo almost periodic solutions for some partial functional differential equations , 2009 .

[34]  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 .

[35]  Zhang Chuanyi.  Almost Periodic Type Functions and Ergodicity , 2003 .

[36]  Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems , 2007 .

[37]  Zhanji Gui,et al.  Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays , 2009 .

[38]  Bingwen Liu,et al.  Global Exponential Stability of Pseudo Almost Periodic Solutions for SICNNs with Time-Varying Leakage Delays , 2014 .

[39]  T. Diagana.  Existence and uniqueness of pseudo-almost periodic solutions to some classes of partial evolution equations , 2007 .

[40]  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..

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

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

[43]  Hui Li,et al.  Anti-periodic solutions for high-order Hopfield neural networks with impulses , 2014, Neurocomputing.

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

[45]  Jinde Cao,et al.  Stability and periodicity in delayed cellular neural networks with impulsive effects , 2007 .

[46]  Changjin Xu,et al.  Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays , 2014, Network.

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

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

[49]  F. Chérif.  Pseudo almost periodic solution of Nicholson’s blowflies model with mixed delays , 2015 .

[50]  Jiyu Wang,et al.  An analysis on the global exponential stability and the existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses , 2008, Comput. Math. Appl..

[51]  Yiguang Liu,et al.  Multi-stability and almost periodic solutions of a class of recurrent neural networks , 2007 .

[52]  Cheng Shao,et al.  Delay-dependent stability criterion for delayed Hopfield neural networks , 2009 .

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

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

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

[56]  Jianying Shao.  Pseudo almost periodic solutions for a Lasota-Wazewska model with an oscillating death rate , 2015, Appl. Math. Lett..

[58]  Farouk Chérif,et al.  Existence and global exponential stability of pseudo almost periodic solution for SICNNs with mixed delays , 2012 .