Anti-periodic mild attractor of delayed hopfield neural networks systems with reaction-diffusion terms

In this paper, reaction-diffusion Hopfield neural networks systems with time-varying delays and Dirichlet boundary conditions are investigated. The theorems on existence and global exponential stability of anti-periodic mild solution are established. Moreover, theoretical results further show that diffusion terms contribute to existence and stabilization of anti-periodic mild solution. Finally, an illustrative example and numerical simulations are given to show effectiveness of results in this paper.

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

[2]  Zaitang Huang,et al.  Existence and exponential stability of almost periodic solution for stochastic cellular neural networks with delay , 2009 .

[3]  Eva Kaslik,et al.  Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis , 2011, Neural Networks.

[4]  Yuqing Chen,et al.  Anti-periodic solutions for fully nonlinear first-order differential equations , 2007, Math. Comput. Model..

[5]  Weirui Zhao.  Dynamics of Cohen–Grossberg neural network with variable coefficients and time-varying delays , 2008 .

[6]  Yonghui Xia,et al.  Impulsive effect on the delayed Cohen-Grossberg-type BAM neural networks , 2010, Neurocomputing.

[7]  Tianping Chen,et al.  Global exponential stability of almost periodic solution for a large class of delayed dynamical systems , 2005 .

[8]  T. Diagana,et al.  SQUARE-MEAN ALMOST PERIODIC SOLUTIONS NONAUTONOMOUS STOCHASTIC DIFFERENTIAL EQUATIONS , 2007 .

[9]  Pagavathigounder Balasubramaniam,et al.  Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays , 2008, Appl. Math. Comput..

[10]  Jinde Cao,et al.  Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms , 2005 .

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

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

[13]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[14]  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.

[15]  Lihong Huang,et al.  Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays☆ , 2009 .

[16]  Neyir Ozcan,et al.  A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays , 2009 .

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

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

[19]  Leon O. Chua,et al.  Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation , 1995 .

[20]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[21]  Jianhua Huang,et al.  Uniform attractors for non-autonomous parabolic equations with delays ☆ , 2009 .

[22]  Lihong Huang,et al.  Anti-periodic solutions for a class of Liénard-type systems with continuously distributed delays , 2009 .

[23]  Yongkun Li.  Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays , 2004 .

[24]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[25]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[26]  Jiong Ruan,et al.  Almost periodic attractor for Cohen–Grossberg neural networks with delay , 2009 .

[28]  Hongyong Zhao,et al.  Existence and stability of almost periodic solution for Cohen–Grossberg neural networks with variable coefficients☆ , 2008 .

[29]  Zidong Wang,et al.  State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case , 2009, IEEE Transactions on Neural Networks.

[30]  LU Wenlian Chen Tianping,et al.  Global exponential stability of almost periodic solution for a large class of delayed dynamical systems , 2005 .

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

[32]  Jinde Cao,et al.  On periodic solutions of neural networks via differential inclusions , 2009, Neural Networks.

[33]  Kelin Li,et al.  Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms , 2008, Neurocomputing.

[34]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[35]  Jianying Shao,et al.  An anti-periodic solution for a class of recurrent neural networks , 2009 .

[36]  Haydar Akça,et al.  SPATIAL DISCRETIZATION OF AN IMPULSIVE COHEN-GROSSBERG NEURAL NETWORK WITH TIME - VARYING AND DISTRIBUTED DELAYS AND REACTION - DIFFUSION TERMS , 2009 .

[37]  陈安平.  EXISTENCE AND ATTRACTIVITY OF ALMOST PERIODIC SOLUTION FOR HOPFIELD NEURAL NETWORKS WITH VARIABLE COEFFICIENTS , 2003 .

[38]  Jinde Cao,et al.  Existence and stability of almost periodic solution for BAM neural networks with delays , 2003, Appl. Math. Comput..

[39]  Yurong Liu,et al.  State estimation for jumping recurrent neural networks with discrete and distributed delays , 2009, Neural Networks.

[40]  Zhidong Teng,et al.  Global exponential synchronization in delayed reaction-diffusion cellular neural networks with the Dirichlet boundary conditions , 2010, Math. Comput. Model..

[41]  Daoyi Xu,et al.  Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays , 2003, Science in China Series F: Information Sciences.

[42]  Bernabé Linares-Barranco,et al.  Log-domain implementation of complex dynamics reaction-diffusion neural networks , 2003, IEEE Trans. Neural Networks.

[43]  Junguo Lu.  Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[44]  Simeon Reich,et al.  Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities , 2001 .

[45]  Xiwei Liu,et al.  Synchronization of linearly coupled neural networks with reaction-diffusion terms and unbounded time delays , 2010, Neurocomputing.

[46]  Walter Allegretto,et al.  Stability for delayed reaction–diffusion neural networks , 2007 .

[47]  Yan Wang,et al.  Antiperiodic solutions for dissipative evolution equations , 2010, Math. Comput. Model..

[48]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

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

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

[51]  Kai Liu,et al.  Existence, Uniqueness, and Asymptotic Behavior of Mild Solutions to Stochastic Functional Differential Equations in Hilbert Spaces , 2002 .

[52]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[53]  Wentao Wang.  Anti-periodic solution for impulsive high-order Hopfield neural networks with time-varying delays in the leakage terms , 2013 .

[54]  Zhidong Teng,et al.  Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms , 2010, IEEE Transactions on Neural Networks.