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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 573534, 18 pages
http://dx.doi.org/10.1155/2009/573534
Research Article

Existence and Exponential Stability of Periodic Solution of High-Order Hopfield Neural Network with Delays on Time Scales

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received 17 April 2009; Accepted 3 August 2009

Academic Editor: Binggen Zhang

Copyright © 2009 Yongkun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [15 citations]

The following is the list of published articles that have cited the current article.

  • Kaihong Zhao, and Yongkun Li, “Existence and Global Exponential Stability of Equilibrium Solution to Reaction-Diffusion Recurrent Neural Networks on Time Scales,” Discrete Dynamics In Nature And Society, 2010. View at Publisher · View at Google Scholar
  • Yongkun Li, and Jiangye Shu, “Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales,” Communications In Nonlinear Science And Numerical Simulation, vol. 16, no. 8, pp. 3326–3336, 2011. View at Publisher · View at Google Scholar
  • Yongkun Li, and Kaihong Zhao, “Robust stability of delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales,” Neurocomputing, vol. 74, no. 10, pp. 1632–1637, 2011. View at Publisher · View at Google Scholar
  • Lili Zhao, and Yongkun Li, “Existence and Exponential Stability of Anti-periodic Solutions of High-order Hopfield Neural Networks with Delays on Time Scales,” Differential Equations and Dynamical Systems, vol. 19, no. 1-2, pp. 13–26, 2011. View at Publisher · View at Google Scholar
  • Yupei Lv, Bo Zhou, and Qiankun Song, “Stability of neural networks with both impulses and time-varying delays on time scale,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6675, no. 1, pp. 203–212, 2011. View at Publisher · View at Google Scholar
  • Yongkun Li, and Chao Wang, “Almost Periodic Functions on Time Scales and Applications,” Discrete Dynamics in Nature and Society, 2011. View at Publisher · View at Google Scholar
  • Yongkun Li, and Chao Wang, “Almost periodic solutions of shunting inhibitory cellular neural networks on time scales,” Communications In Nonlinear Science And Numerical Simulation, vol. 17, no. 8, pp. 3258–3266, 2012. View at Publisher · View at Google Scholar
  • Yongkun Li, Kaihong Zhao, and Yuan Ye, “Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales,” Neural Processing Letters, vol. 36, no. 3, pp. 217–234, 2012. View at Publisher · View at Google Scholar
  • Meng Hu, and Lili Wang, “Dynamic Inequalities on Time Scales with Applications in Permanence of Predator-Prey System,” Discrete Dynamics in Nature and Society, vol. 2012, pp. 1–15, 2012. View at Publisher · View at Google Scholar
  • Yongkun Li, and Li Yang, “Almost automorphic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales,” Applied Mathematics and Computation, vol. 242, pp. 679–693, 2014. View at Publisher · View at Google Scholar
  • Chao Wang, and Xia Li, “Existence and Global Exponential Stability of Almost Periodic Solution for High-Order BAM Neural Networks with Delays on Time Scales,” Neural Processing Letters, vol. 39, no. 3, pp. 247–268, 2014. View at Publisher · View at Google Scholar
  • Wei Chen, and Shuhua Gong, “Global Exponential Stability of Antiperiodic Solution for Impulsive High-Order Hopfield Neural Networks,” Abstract and Applied Analysis, vol. 2014, pp. 1–11, 2014. View at Publisher · View at Google Scholar
  • Lili Zhao, and Yongkun Li, “Global Exponential Stability of Weighted Pseudo-Almost Periodic Solutions of Neutral Type High-Order Hopfield Neural Networks with Distributed Delays,” Abstract and Applied Analysis, vol. 2014, pp. 1–17, 2014. View at Publisher · View at Google Scholar
  • Li Yang, and Yongkun Li, “Existence and exponential stability of periodic solution for stochastic hopfield neural networks on time scales,” Neurocomputing, 2015. View at Publisher · View at Google Scholar
  • Lili Wang, and Meng Hu, “Nabla inequalities and permanence for a logistic integrodifferential equation on time scales,” Open Mathematics, vol. 15, no. 1, pp. 1578–1590, 2017. View at Publisher · View at Google Scholar