International Journal of Modern Education and Computer Science (IJMECS)
IJMECS Vol. 3, No. 5, 8 Oct. 2011
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Stabilitty of Anti-periodic Solutions for Certain Shunting Inhibitory Cellular Neural Networks
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Author(s)
Huiyan Kang
1,*
Ligeng Si
2
Index Terms
Global exponential stability, Shunting inhibitory cellular neural networks, Anti-periodic soluti-on, Continuously distributed delays, Lyapunov fuctions
Abstract
In this paper, the existence and exponential stability of anti-periodic solutions for shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays are considered by constructing suitable Lyapunov fuctions and applying some critial analysis techniques. Our results remove restrictive conditions of the global Lipschitz and bounded conditions of activation functions and new sufficient conditions ensuring the exist-ence and exponential stability of anti-periodic solutions for SICNNs are obtained. Moreover, an example is given to illustrate the feasibility of the conditions in our results.
Cite This Paper
Huiyan Kang, Ligeng Si, "Stabilitty of Anti-periodic Solutions for Certain Shunting Inhibitory Cellular Neural Networks", International Journal of Modern Education and Computer Science(IJMECS), vol.3, no.5, pp.26-32, 2011. DOI:10.5815/ijmecs.2011.05.04
Reference
[1]A. Bouzerdoum , R.B. Pinter , “Shunting inhibitory cellular neural networks: Derivation and stability analysis”, IEEE Trans. Circuits Syst1-Fundamental Theory and Applications , vol. 40,1993, pp. 215-221.
[2]A. Bouzerdoum, R.B. Pinter, “Analysis and analog implem-entation of directionally sensitive shunting inhibitory cellular neural networks ”, Visual Information Processing: From neurons to Chips SPIE, vol..1473, 1991, pp. 29-38.
[3]A. Bouzerdoum , R.B. Pinter , “Nonlinear lateral inhibition applied to motion detection in the fly visual system”, in: R. B. Pinter , B. Nabet (Eds.), Nonlinear Vision, CRC Press , Boca Raton, FL, 1992, pp. 423-450.
[4]A. Chen , J. Cao , L. Huang , “Almost periodic solution of shunting inhibitory CNNs with delays ”, Physics Letters , vol.. A298 , 2002 , pp. 161-170.
[5]Y. Li , C. Liu , L..Zhu , “ Global exponential stability of periodic solution of shunting inhibitory CNNs with delays”, Physics Letters , vol.. A337, 2005, pp. 46-54.
[6]B. Liu, L. Huang, “Existence and stability of almost Periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays”, Physics Letters, vol. A349, 2006, pp.177-186.
[7]Q.Zhou, B.Xiao, Y.Yu, L.Peng, “Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural net works with continuously distributed delays”, Chaos, Solitons and Fractals, vol. 34 , 2007, pp. 860-866.
[8]M. Cai , H. Hong , Z. Yuan , “Positive almost periodic solution of shunting inhibitory cellular neural networks with time-varying delays”, Mathematics and Computers in Simulation, vol. 78, 2008, pp. 548-558.
[9]Y.Liu, Z.You, L.Cao, “Almost periodic solution of Shunting inhibitory cellular neural networks with time varying and continuously distributed delays”, Physics Letters, vol. A364, 2007, pp. 17-28.
[10]Q. Fan, J. Shao, “ Almost periodic solution of shunting Inhibitory cellular neural networks with timevarying and continuously distributed delays”, Commun Nonlinear Sci Nu-mer Simulat, vol..15, 2010, pp. 1655-1663.
[11]B.Liu , “ stability of shunting inhibitory cellular neural networks with unbounded time-varying delays ”, Applied Ma-thematics Letters,vol. 22, 2009, pp.1-5.
[12]J.Shao, L.Wang, C.Ou, “ Almost periodic solution for shunting inhibitory cellular neural networks without global Lipschitz activaty functions ”, Applied Mathematics Modelling , vol. 33, 2009, pp. 2575-2581.
[13]C.Ou, “Almost periodic solution for shunting inhibitory cellular neural networks”, Nonlinear Analysis: Real World Applications, vol.. 10, 2009, 2652-2658.
[14]J.Shao , “ Anti-periodic solution for shunting inhibitory cellular neural networks with time-varying delays”, Physics Letters, vol. A372, 2008, 5011-5016.
[15]G.Peng , L.Huang, “ Anti-periodic solution for shunting Inhibitory cellular neural networks with continuously distributed delays ” , Nonlinear Analysis: Real World Applications, vol.10, 2009, pp. 2434-2440.
[16]J.Shao , “ An Anti-periodic solution for a class of recurrent Neural networks ”, Journal of Computional and Applied Mathematics , vol. 228 , 2009, pp. 231-237.
[17]R. Wu , “An anti-periodic LaSalle oscillation theorem ”, Applied Mathematics Letters, vol. 21, 2008, pp.928-933.
[18]J.K. Hale, Theory of Functional Differential Equa-tions, Springer-Verlag ,New York, 1977.