Weighted pseudo-almost automorphic solutions of high-order Hopfield neural networks with neutral distributed delays

In this paper, a class of high-order Hopfield neural networks with neutral distributed delays is considered. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of weighted pseudo-almost automorphic solutions for this class of networks by employing the Banach fixed-point theorem and differential inequality techniques. The results of this paper are completely new. An example is given to show the effectiveness of the proposed method and results.

[1]  Huaguang Zhang,et al.  Novel Delay-Dependent Robust Stability Analysis for Switched Neutral-Type Neural Networks With Time-Varying Delays via SC Technique , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[3]  Huaguang Zhang,et al.  Novel Exponential Stability Criteria of High-Order Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Linshan Wang,et al.  Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays , 2011 .

[5]  Bingji Xu,et al.  Global asymptotic stability of high-order Hopfield type neural networks with time delays , 2003 .

[6]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Toka Diagana,et al.  Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations , 2011 .

[8]  Gisèle Mophou,et al.  Weighted pseudo almost automorphic functions and applications to abstract differential equations , 2009 .

[9]  Xin Wang,et al.  Impulsive stabilization and synchronization of Hopfield-type neural networks with impulse time window , 2017, Neural Computing and Applications.

[10]  Toka Diagana,et al.  Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces , 2013 .

[11]  Li Yang,et al.  Almost automorphic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales , 2014, Appl. Math. Comput..

[12]  Yongkun Li,et al.  Existence of periodic solutions for neutral type cellular neural networks with delays , 2012 .

[13]  Zhenyuan Guo,et al.  Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations , 2014 .

[14]  Yurong Liu,et al.  Almost periodic solution for a neutral-type neural networks with distributed leakage delays on time scales , 2016, Neurocomputing.

[15]  Chuanyi Zhang,et al.  Translation invariance of weighted pseudo almost periodic functions and related problems , 2012 .

[16]  Jin Liang,et al.  Decomposition of weighted pseudo-almost periodic functions , 2010 .

[17]  Hairong Dong,et al.  Adaptive neural control with intercepted adaptation for time-delay saturated nonlinear systems , 2015, Neural Computing and Applications.

[18]  Bo Song,et al.  Stability analysis of Hopfield neural networks perturbed by Poisson noises , 2016, Neurocomputing.

[19]  Toka Diagana.  Doubly-Weighted Pseudo-Almost Periodic Functions , 2010 .

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

[21]  Pagavathigounder Balasubramaniam,et al.  LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays , 2008, Appl. Math. Comput..

[22]  Manolis A. Christodoulou,et al.  Structural properties of gradient recurrent high-order neural networks , 1995 .

[23]  Toka Diagana,et al.  Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with Sp-weighted pseudo-almost periodic coefficients , 2010 .

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

[25]  Yanli Xu.  Anti-periodic solutions for HCNNs with time-varying delays in the leakage terms , 2012, Neural Computing and Applications.

[26]  Yongkun Li,et al.  Existence and exponential stability of almost periodic solution for neutral delay BAM neural networks with time-varying delays in leakage terms , 2013, J. Frankl. Inst..

[27]  Jianlong Qiu,et al.  Dynamics of high-order Hopfield neural networks with time delays , 2010, Neurocomputing.

[28]  Ju H. Park,et al.  A novel delay-dependent criterion for delayed neural networks of neutral type , 2010 .

[29]  Toka Diagana.  Existence of Doubly-Weighted Pseudo Almost Periodic Solutions to Some Classes of Nonautonomous Differential Equations , 2010 .

[30]  Pagavathigounder Balasubramaniam,et al.  New global exponential stability results for neutral type neural networks with distributed time delays , 2008, Neurocomputing.

[31]  Ju H. Park,et al.  A new stability criterion for bidirectional associative memory neural networks of neutral-type , 2008, Appl. Math. Comput..

[32]  Jinde Cao,et al.  Global exponential stability results for neutral-type impulsive neural networks , 2010 .

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