Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Existence and Exponential Stability of Almost Periodic Solution for Recurrent Neural Networks on Time Scales
Abstract:
In this paper, a class of recurrent neural networks (RNNs) with variable delays are studied on almost periodic time scales, some sufficient conditions are established for the existence and global exponential stability of the almost periodic solution. These results have important leading significance in designs and applications of RNNs. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.
Keywords: Recurrent neural network, Almost periodic solution, Global exponential stability, Time scale.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062020
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1413References:
[1] V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
[2] A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
[3] X. Liu, Advances in Impulsive Differential Equations, Dynamics of Continuous, Discrete Impulsive System. Series A. Math. Anal. 9 (2002) 313-462.
[4] W. Zhang and M. Fan, Periodicity in generalized ecological competition sysytem governed by impulsive differential equations with delays, Math. Comput. Modelling 39 (2004) 479-493.
[5] R.P. Agarwal and D.O-Regan, Multiple nonnegative solutions for second order impulsive differential equations, Appl. Math. Comput. 114 (2000) 51-59.
[6] Z. He and X. Zhang, Monotone iterative technique for first order impulsive differential equations with periodic boundary conditions, Appl. Math. Comput. 156 (2004) 605-620.
[7] M. Bohner, A. Peterson, Advances in dynamic equations on time scales, Boston: Birkh¨auser, 2003.
[8] S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results in Mathematics 18 (1990) 18-56.
[9] R. McKcllar, K. Knight, A combined discrete-continuous model describing the lag phase of listeria monocytogenes, Int. J. Food Microbiol., 54(3) (2000) 171-180.
[10] C. Tisdell, A. Zaidi, Basic qualitative and qualitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling, Nonlinear Anal. Theor., 68(11) (2008) 3504-3524.
[11] M. Fazly, M. Hesaaraki, Periodic solutions for predator-prey systems with Beddington-DeAngelis functional response on time scales, Nonlinear Anal. Real., 9(3) (2008) 1224-1235.
[12] Y. Li, M. Hu, Three positive periodic solutions for a class of higherdimensional functional differential equations with impulses on time scales, Advances in Difference Equations, 2009, Article ID 698463.
[13] Y. Li, C. Wang, Almost periodic functions on time scales and applications, Discrete Dynamics in Nature and Society, Volume 2011, Article ID 727068.
[14] M. Hu, L. Wang, Unique existence theorem of solution of almost periodic differential equations on time scales, Discrete Dynamics in Nature and Society, Volume 2012, Article ID 240735.