Periodic Solutions of Recurrent Neural Networks with Distributed Delays and Impulses on Time Scales
In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061292Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1273
 J. Can, J. Wang, Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I 52 (5) (2005) 417-425.
 H. Huang, J. Cao and J. Wang, Global exponential stability and periodic solutions of recurrent neural networks with delays, Phys. Lett. A 298 (5-6) (2002) 393-404.
 Y.Y. Wu, Y.Q. Wu, Stability Analysis for Recurrent Neural Networks with Time-varying Delay, International Journal of Automation and Computing 6 (3) (2009) 223-227.
 Y.Y. Wu, T. Li, Y.Q. Wu, Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays, International Journal of Automation and Computing 7 (2) (2010) 199-204.
 C. Xing, Z. Gui, Global Asymptotic Stability of Recurrent Neural Networks with Time-Varying Delays and Impulses, Fourth International Conference on Natural Computation 2 (2008) 394-398.
 H.G. Zhang, Z.S. Wang, New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay, Sci. China. Ser. F-Inf. Sci. 52 (6) (2009) 942-948.
 J. Can, D.S. Huang, Y.Z. Qu, Global robust stability of delayed recurrent neural networks, Chaos, Solitons and Fractals 23 (2005) 221-229.
 J. Can, J. Wang, Global exponential stability and periodicity of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I 52 (5) (2005) 920-931.
 H.A. Jalab, R.W. Ibrahim, Stability of recurrent neural networks, Int. J. Comp. Sci. Net. Sec. 12 (6) (2006) 159-164.
 J. Cao, J. Wang, Absolute exponential stability of recurrent neural networks with lipschitz-continuous activation functions and time-varying delays, Neural Networks 17 (2004) 379-390.
 Y. Li, L. Lu, Global exponential stability and existence of periodic solutions of Hopfield-type neural networks with impulses, Phys. Lett. A 333 (2004) 62-71.
 Y. Li, S. Gao, Global Exponential Stability for Impulsive BAM Neural Networks with Distributed Delays on Time Scales, Neural Processing Letters 31 (1) (2010) 65-91.
 Y. Li, T. Zhang, Global Exponential Stability of Fuzzy Interval Delayed Neural Networks with impulses on Time Scales, Int. J. Neural Syst. 19 (6) (2009) 449-456.
 Y. Li, X. Chen, L. Zhao, Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales, Neurocomputing 72 (7-9) 1621-1630 (2009).
 Y. Li, L. Zhao, P. Liu, Existence and exponential stability of periodic solution of high-order Hopfield neural network with delays on time scales, Volume 2009 (2009), Article ID 573534, 18 pages.
 J. Dai, Y. Li, T. Zhang, Positive periodic solutions for nonautonomous impulsive neutral functional differential systems with time-varying delays on time scales, 34 (2010) 1-10.
 Y. Li, H. Zhang, Existence of periodic solutions for a periodic mutualism model on time scales, J. Math. Anal. Appl. 343 (2) (2008) 818-825.
 Y. Li, M. Hu, Three Positive Periodic Solutions for a Class of Higher-Dimensional Functional Differential Equations with Impulses on Time Scales, Advances in Difference Equations (2009) doi:10.1155/2009/698463.
 J. Liu, Y. Li, L. Zhao, On a periodic predator-prey system with time delays on time scales, Commun. Nonlinear Sci. Numer. Simulat. 8 (14) (2009) 3432-3438.
 M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
 L. Bi, M. Bohner, M. Fan, Periodic solutions of functional dynamic equations with infinite delay, Nonlinear Anal. 68 (2008) 1226-1245.
 V. Lakshmikantham, A.S. Vatsala, Hybrid systems on time scales, J. Comput. Appl. Math. 141 (2002) 227-235.
 E.R. Kaufmann, Y.N. Raffoul, Periodic solutions for a neutral nonlinear dynamic equation on a time scale, J. Math. Anal. Appl. 319 (2006) 315- 25.
 M. Bohner, M. Fan, J.M. Zhang, Existence of periodic solutions in predator-prey and competetion dynamic systems, Nonlinear Anal. Real Word Appl. 330 (1) (2007) 1-9.
 F.H. Wang, C.C. Yeh, S.L. Yu, C.H. Hong, Youngs inequality and related results on time scales, Appl. Math. Lett. 18 (2005) 983-988.
 J.L. Mawhin, Topological degree methods in noninear boundary value problems, CBMS Regional Conference Series in Mathematics, No. 40, American Mathematical Society, Provedence, RI, 1979.
 D. O,regan, Y.J. Chao, Y.Q. Chen, Topological degree theory and application, Taylor and Francis Group, Boca Raton, London, New York, 2006.
 A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Science, Academic Press, New York, 1979.