Anti-periodic Solutions for Cohen-Grossberg Shunting Inhibitory Neural Networks with Delays
By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.
[1] M.A. Cohen, S. Grossberg, Absolute stability and global pattern formation
and parallel memory storage by competitive neural networks, IEEE Trans.
Syst. Man. Cybern. 13 (1983) 815-826.
[2] W.R. Zhao, Global exponential stability analys is of Cohen-Grossberg
neural network with delays, Commun. Nonlinear Sci. Numer. Simulat.
13(2008) 847-856.
[3] K. Yuan, J. Cao, Ananalysis of global asymptotic stability of delayed
Cohen-Grossberg neural networks via nonsmoothan alysis, IEEE Trans.
CAS-I 52 (9)(2005) 1854-1861.
[4] J. Cao, G. Feng, Y. Wang, Multistability and multi periodicity of delayed
Cohen-Grossberg neural networks with ageneral class of activation
functions, Physica D 237 (13) (2008) 1734-1749.
[5] F. Tu, X. Liao, Harmless delays for global asymptotic stability of Cohen-
Grossberg neural networks, Chaos Solitons Fractals 26 (2005) 927-933.
[6] Y. Li, Existence and stability of periodic solutions for Cohen-Grossberg
neural networks with multiple delays, Chaos Solitons Fractals 20 (2004)
459-466.
[7] W. Wu, B.T. Cui, M. Huang, Global asymptotic stability of delayed
Cohen-Grossberg neural networks, Chaos Solitons Fractals 34 (2007)
872-877.
[8] B.W. Liu, L.H. Huang, Existence and global exponential stability of
periodic solutions for a class of Cohen-Grossberg neural networks with
time-varying delays, Chaos Solitons Fractals 32 (2007) 617-627.
[9] Y. Li, X. Fan, Existence and globally exponential stability of almost periodic
solution for Cohen-Grossberg BAM neural networks with variable
coefficients, Appl. Math. Modelling 33 (2009) 2114-2120.
[10] 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 (2009) 1621-1630.
[11] C. Li, Y. Li, Y. Ye, Exponential stability of fuzzy Cohen-Grossberg neural
networks with time delays and impulsive effects, Commun. Nonlinear
Sci. Numer. Simulat. 15 (2010) 3599-3606.
[12] Y. Li, C. Liu, L. Zhu, Global exponential stability of periodic solution
for shunting inhibitory CNNs with delays, Phys. Lett. A 337 (2005) 46-
54.
[13] X.S. Yang, Existence and global exponential stability of periodic solution
for Cohen-Grossberg shunting inhibitory cellular neural networks with
delays and impulses, Neurocomputing 72 (2009) 2219-2226.
[14] Y.H. Xia, J.D. Cao, Z.K. Huang, Existence and exponential stability of
almost periodic solution for shunting inhibitory cellular neural networks
with impulses, Chaos, Solitons Fractals 34 (2007) 1599-1607.
[15] L. Chen, H.Y. Zhao, Global stability of almost periodic solution of
shunting inhibitory cellular neural networks with variable coecients,
Chaos, Solitons Fractals 35 (2008) 351-357.
[16] J.Y. Shao, An anti-periodic solution for a class of recurrent neural
networks, J. Comput. Appl. Math. 228 (2009) 231-237.
[17] J.Y. Shao, Anti-periodic solutions for shunting inhibitory cellular neural
networks with time-varying delays, Phys. Lett. A 372 (2008) 5011-5016.
[18] Y.K. Li, L. Yang, Anti-periodic solutions for Cohen-Grossberg neural
networks with bounded and unbounded delays, Commun. Nonlinear Sci.
Numer. Simulat. 14 (2009) 3134-3140.
[19] G.Q. Peng, L.H. Huang, Anti-periodic solutions for shunting inhibitory
cellular neural networks with continuously distributed delays, Nonlinear
Anal.: Real World Appl. 10 (2009) 2434-2440.
[20] Q.Y. Fan, W.T. Wang, X.J. Yi, Anti-periodic solutions for a class of
nth-order differential equations with delay, J. Comput. Appl. Math. 230
(2009) 762-769.
[21] D. O-regan, Y.J. Cho, Y.Q. Chen, Topological degree theory and application,
Taylor & Francis Group, Boca Raton, London, New York, 2006.
[1] M.A. Cohen, S. Grossberg, Absolute stability and global pattern formation
and parallel memory storage by competitive neural networks, IEEE Trans.
Syst. Man. Cybern. 13 (1983) 815-826.
[2] W.R. Zhao, Global exponential stability analys is of Cohen-Grossberg
neural network with delays, Commun. Nonlinear Sci. Numer. Simulat.
13(2008) 847-856.
[3] K. Yuan, J. Cao, Ananalysis of global asymptotic stability of delayed
Cohen-Grossberg neural networks via nonsmoothan alysis, IEEE Trans.
CAS-I 52 (9)(2005) 1854-1861.
[4] J. Cao, G. Feng, Y. Wang, Multistability and multi periodicity of delayed
Cohen-Grossberg neural networks with ageneral class of activation
functions, Physica D 237 (13) (2008) 1734-1749.
[5] F. Tu, X. Liao, Harmless delays for global asymptotic stability of Cohen-
Grossberg neural networks, Chaos Solitons Fractals 26 (2005) 927-933.
[6] Y. Li, Existence and stability of periodic solutions for Cohen-Grossberg
neural networks with multiple delays, Chaos Solitons Fractals 20 (2004)
459-466.
[7] W. Wu, B.T. Cui, M. Huang, Global asymptotic stability of delayed
Cohen-Grossberg neural networks, Chaos Solitons Fractals 34 (2007)
872-877.
[8] B.W. Liu, L.H. Huang, Existence and global exponential stability of
periodic solutions for a class of Cohen-Grossberg neural networks with
time-varying delays, Chaos Solitons Fractals 32 (2007) 617-627.
[9] Y. Li, X. Fan, Existence and globally exponential stability of almost periodic
solution for Cohen-Grossberg BAM neural networks with variable
coefficients, Appl. Math. Modelling 33 (2009) 2114-2120.
[10] 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 (2009) 1621-1630.
[11] C. Li, Y. Li, Y. Ye, Exponential stability of fuzzy Cohen-Grossberg neural
networks with time delays and impulsive effects, Commun. Nonlinear
Sci. Numer. Simulat. 15 (2010) 3599-3606.
[12] Y. Li, C. Liu, L. Zhu, Global exponential stability of periodic solution
for shunting inhibitory CNNs with delays, Phys. Lett. A 337 (2005) 46-
54.
[13] X.S. Yang, Existence and global exponential stability of periodic solution
for Cohen-Grossberg shunting inhibitory cellular neural networks with
delays and impulses, Neurocomputing 72 (2009) 2219-2226.
[14] Y.H. Xia, J.D. Cao, Z.K. Huang, Existence and exponential stability of
almost periodic solution for shunting inhibitory cellular neural networks
with impulses, Chaos, Solitons Fractals 34 (2007) 1599-1607.
[15] L. Chen, H.Y. Zhao, Global stability of almost periodic solution of
shunting inhibitory cellular neural networks with variable coecients,
Chaos, Solitons Fractals 35 (2008) 351-357.
[16] J.Y. Shao, An anti-periodic solution for a class of recurrent neural
networks, J. Comput. Appl. Math. 228 (2009) 231-237.
[17] J.Y. Shao, Anti-periodic solutions for shunting inhibitory cellular neural
networks with time-varying delays, Phys. Lett. A 372 (2008) 5011-5016.
[18] Y.K. Li, L. Yang, Anti-periodic solutions for Cohen-Grossberg neural
networks with bounded and unbounded delays, Commun. Nonlinear Sci.
Numer. Simulat. 14 (2009) 3134-3140.
[19] G.Q. Peng, L.H. Huang, Anti-periodic solutions for shunting inhibitory
cellular neural networks with continuously distributed delays, Nonlinear
Anal.: Real World Appl. 10 (2009) 2434-2440.
[20] Q.Y. Fan, W.T. Wang, X.J. Yi, Anti-periodic solutions for a class of
nth-order differential equations with delay, J. Comput. Appl. Math. 230
(2009) 762-769.
[21] D. O-regan, Y.J. Cho, Y.Q. Chen, Topological degree theory and application,
Taylor & Francis Group, Boca Raton, London, New York, 2006.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53398", author = "Yongkun Li and Tianwei Zhang and Shufa Bai", title = "Anti-periodic Solutions for Cohen-Grossberg Shunting Inhibitory Neural Networks with Delays", abstract = "By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.
", keywords = "Anti-periodic solution, coincidence degree, global exponential stability, Cohen-Grossberg shunting inhibitory cellular neural networks.", volume = "4", number = "3", pages = "345-6", }
