Existence and Exponential Stability of Almost Periodic Solution for Recurrent Neural Networks on Time Scales
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.
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Differential Equations, World Scientific, Singapore, 1989.
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World Scientific, Singapore, 1995.
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Continuous, Discrete Impulsive System. Series A. Math. Anal. 9 (2002)
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sysytem governed by impulsive differential equations with delays, Math.
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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.
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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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55054", author = "Lili Wang and Meng Hu", title = "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.", volume = "6", number = "8", pages = "950-5", }
