ON PERIODIC DYNAMICAL SYSTEMS

Abstract

Chinese Annals of MathematicsVol. 25, No. 04, pp. 455-462 (2004) No AccessON PERIODIC DYNAMICAL SYSTEMSWENLIAN LU and TIANPING CHENWENLIAN LULaboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433, China Search for more papers by this author and TIANPING CHENLaboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433, China Search for more papers by this author https://doi.org/10.1142/S025295990400041XCited by:27 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe authors investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the results obtained are universal.Project supported by the National Natural Science Foundation of China (No.69982003, No.60074005) and the Graduate Innovation Foundation of Fudan University.Keywords:Neural networkDynamical systemsPeriodic solutionGlobal convergence2000 MR Subject Classification 34K132000 MR Subject Classification 34K252000 MR Subject Classification 34K60 References T. P. Chen, W. L. Lu and G. R. Chen, Neural Computation (2004). Google ScholarK. Gopalsamy and Sariyasa, IEEE Transactions on Neural Networks 13(2), 551 (2002). Crossref, Google ScholarZ. G. Liu and L. S. Liao, J. Math. Annl. Appl. 290, 247 (2004). Crossref, Google ScholarS. Mohamad and K. Gopalsamy, Dis. Cont. Dyn. Syst. 6, 841 (2000). Crossref, Google ScholarY. Zhang, IEEE Transactions Cirsuits and Systems I 49, 256 (2002). Crossref, Google ScholarY. X. Zheng and T. P. Chen, Physics Letters A 322(5-6), 344 (2004). Crossref, Google ScholarJ. Zhou, Z. R. Liu and G. R. Chen, Neural Networks 17(1), 87 (2004). Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 27Incremental Stability of Neural Networks with Switched Parameters and Time Delays via Contraction Theory of Multiple NormsHao Qiang and Wenlian Lu18 November 2018Lag Synchronization of Memristor-Based Coupled Neural Networks via -MeasureNing Li and Jinde Cao1 Mar 2016 | IEEE Transactions on Neural Networks and Learning Systems, Vol. 27, No. 3Survey of Dynamics of Cohen–Grossberg-Type RNNsZhanshan Wang, Zhenwei Liu and Chengde Zheng19 July 2015New criterion of asymptotic stability for delay systems with time-varying structures and delaysBo Liu, Wenlian Lu and Tianping Chen1 Jun 2014 | Neural Networks, Vol. 54Convergence behavior of delayed discrete cellular neural network without periodic coefficientsJinling Wang, Haijun Jiang, Cheng Hu and Tianlong Ma1 May 2014 | Neural Networks, Vol. 53Generalized Halanay Inequalities and Their Applications to Neural Networks With Unbounded Time-Varying Delays Bo Liu, Wenlian Lu and Tianping Chen1 Sep 2011 | IEEE Transactions on Neural Networks, Vol. 22, No. 9LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures Zhanshan Wang, Huaguang Zhang and Bin Jiang1 Jul 2011 | IEEE Transactions on Neural Networks, Vol. 22, No. 7Universal Analysis Method for Stability of Recurrent Neural Networks with Different Multiple DelaysZhanshan Wang, Enlin Zhang, Kuo Yun and Huaguang Zhang1 Jan 2011Nonnegative periodic dynamics of delayed Cohen–Grossberg neural networks with discontinuous activationsXiangnan He, Wenlian Lu and Tianping Chen1 Aug 2010 | Neurocomputing, Vol. 73, No. 13-15Stability Analysis of Recurrent Neural Networks with Distributed Delays Satisfying Lebesgue-Stieljies MeasuresZhanshan Wang, Huaguang Zhang and Jian Feng1 Jan 2010Convergence behavior of delayed bidirectional associative memory cellular neural networks with asymptotically periodic coefficientsJunyan Xu, Lijuan Chen and Zhong Li1 Oct 2009 | Applied Mathematics and Computation, Vol. 215, No. 3Nonnegative Periodic Dynamics of Cohen-Grossberg Neural Networks with Discontinuous Activations and Discrete Time DelaysXiangnan He, Wenlian Lu and Tianping Chen1 Jan 2009Global Convergent Dynamics of Delayed Neural NetworksWenlian Lu and Tianping Chen29 January 2010Convergence behavior of delayed cellular neural networks without periodic coefficientsJinglei Zhou, Qingguo Li and Fuxing Zhang1 Oct 2008 | Applied Mathematics Letters, Vol. 21, No. 10Almost Periodic Dynamics of a Class of Delayed Neural Networks with Discontinuous ActivationsWenlian Lu and Tianping Chen1 Apr 2008 | Neural Computation, Vol. 20, No. 4Comment on “Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks” [Phys. 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A 352 (2006) 341]Tianping Chen1 Mar 2008 | Physics Letters A, Vol. 372, No. 10Multiple Almost Periodic Solutions in Nonautonomous Delayed Neural NetworksKuang-Hui Lin and Chih-Wen Shih1 Dec 2007 | Neural Computation, Vol. 19, No. 12Dynamics of Cohen–Grossberg neural networks with variable and distributed delaysZisen Mao, Hongyong Zhao and Xiaofeng Wang1 Oct 2007 | Physica D: Nonlinear Phenomena, Vol. 234, No. 1Stability of Cohen-Grossberg Neural Networks with Nonnegative Periodic solutionsTianping Chen and Yanchun Bai1 Aug 2007Global dynamic analysis of general Cohen–Grossberg neural networks with impulseZhang Chen and Jiong Ruan1 Jun 2007 | Chaos, Solitons & Fractals, Vol. 32, No. 5Periodic Solution of Cohen-Grossberg Neural Networks with Variable CoefficientsHongjun Xiang and Jinde Cao1 Jan 2007Existence and Stability of Periodic Solutions for Cohen-Grossberg Neural Networks with Less Restrictive AmplificationHaibin Li and Tianping Chen1 Jan 2007Global Asymptotical Stability of Cohen-Grossberg Neural Networks with Time-Varying and Distributed DelaysTianping Chen and Wenlian Lu1 Jan 2006Existence and Global Stability Analysis of Almost Periodic Solutions for Cohen-Grossberg Neural NetworksTianping Chen, Lili Wang and Changlei Ren1 Jan 2006A Priori Bounds for Periodic Solutions of a Kind of Second Order Neutral Functional Differential Equation with Multiple Deviating ArgumentsShi Ping Lu and Wei Gao Ge4 August 2005 | Acta Mathematica Sinica, English Series, Vol. 21, No. 6Universal Approach to Study Delayed Dynamical SystemsTianping Chen1 Jan 2005Positive periodic solutions of delayed periodic Lotka–Volterra systemsWei Lin and Tianping Chen1 Jan 2005 | Physics Letters A, Vol. 334, No. 4 Recommended Vol. 25, No. 04 Metrics History Received 25 March 2004 KeywordsNeural networkDynamical systemsPeriodic solutionGlobal convergence2000 MR Subject Classification 34K132000 MR Subject Classification 34K252000 MR Subject Classification 34K60PDF download