Existence and Global Exponential Stability of Periodic Solutions of Cellular Neural Networks with Distributed Delays and Impulses on Time Scales
In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.
[1] J. Cao, New results concerning exponential stability and periodic solutions
of delayed cellular neural networks with delays, Phys Lett A 307 (2003)
136-147.
[2] 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.
[3] Z. Liu and A. Chen, Existence and global exponential stability of periodic
solutions of cellular neural networks with time-vary delays, J. Math Anal.
Appl. 290 (2004) 247-262.
[4] Y. Li, Existence and stability of periodic solutions for Cohen¨CGrossberg
neural networks with multiple delays. Chaos, Solitons & Fractals 20
(2004) 459-466.
[5] Y. Li, P. Liu, Existence and stability of positive periodic solution for BAM
neural networks with delays, Math Comput Model 40 (2004) 757-770.
[6] 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.
[7] Y. Li, T. Zhang, Global exponential stability of fuzzy internal delayed
neural networks with impulses on time scales, Int. J. Neural Syst.19 (6)
(2009) 449-456.
[8] Y. Chen, Global stability of neural networks with distributed delays,
Neural Networks 15 (2002) 867-871.
[9] C. Feng, R. Plamondon, On the stability analysis of delayed neural
networks systems, Neural Networks 14 (2011) 1181-1188.
[10] J. Zhang, Globally exponential stability of neural networks with variables
delays. IEEE Trans Circuit Syst-I 50 (2003) 288-291.
[11] Y. Li, Global exponential stability of BAM neural networks with delays
and impulses, Chaos, Solitons & Fractals 24 (2005) 279-285.
[12] Y. Ren, Y. Li, Periodic solutions of recurrent neural networks with
distributed delays and impulses on time scales, Int. J. Comp. Math. Sci.
5 (2011) 209-218.
[13] Z. Guan, L. James, G. Chen, On impulsive auto-associative neural
networks, Neural Networks 13 (2000) 63-69.
[14] Y. Li, W. Xing, L. Lu, Existence and global exponential stability of
periodic solution of a class of neural networks with impulses, Chaos,
Solitons & Fractals 27 (2006) 437-445.
[15] Y. Li, W. Xing, Existence and global exponential stability of periodic
solution of CNNs with impulses, Chaos, Solitons & Fractals 33 (2007)
1686-1693.
[16] R. Gains, J. Mawhin, Coincidence degree and nonlinear differential
equations, Springer-Verlag, Berlin, 1977.
[17] H. Tokumarn, N. Adachi, T. Amemiya, Macroscopic stability of interconnected
systems, 6th IFAC Congress, paper ID44.4, 1975, 1-7.
[1] J. Cao, New results concerning exponential stability and periodic solutions
of delayed cellular neural networks with delays, Phys Lett A 307 (2003)
136-147.
[2] 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.
[3] Z. Liu and A. Chen, Existence and global exponential stability of periodic
solutions of cellular neural networks with time-vary delays, J. Math Anal.
Appl. 290 (2004) 247-262.
[4] Y. Li, Existence and stability of periodic solutions for Cohen¨CGrossberg
neural networks with multiple delays. Chaos, Solitons & Fractals 20
(2004) 459-466.
[5] Y. Li, P. Liu, Existence and stability of positive periodic solution for BAM
neural networks with delays, Math Comput Model 40 (2004) 757-770.
[6] 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.
[7] Y. Li, T. Zhang, Global exponential stability of fuzzy internal delayed
neural networks with impulses on time scales, Int. J. Neural Syst.19 (6)
(2009) 449-456.
[8] Y. Chen, Global stability of neural networks with distributed delays,
Neural Networks 15 (2002) 867-871.
[9] C. Feng, R. Plamondon, On the stability analysis of delayed neural
networks systems, Neural Networks 14 (2011) 1181-1188.
[10] J. Zhang, Globally exponential stability of neural networks with variables
delays. IEEE Trans Circuit Syst-I 50 (2003) 288-291.
[11] Y. Li, Global exponential stability of BAM neural networks with delays
and impulses, Chaos, Solitons & Fractals 24 (2005) 279-285.
[12] Y. Ren, Y. Li, Periodic solutions of recurrent neural networks with
distributed delays and impulses on time scales, Int. J. Comp. Math. Sci.
5 (2011) 209-218.
[13] Z. Guan, L. James, G. Chen, On impulsive auto-associative neural
networks, Neural Networks 13 (2000) 63-69.
[14] Y. Li, W. Xing, L. Lu, Existence and global exponential stability of
periodic solution of a class of neural networks with impulses, Chaos,
Solitons & Fractals 27 (2006) 437-445.
[15] Y. Li, W. Xing, Existence and global exponential stability of periodic
solution of CNNs with impulses, Chaos, Solitons & Fractals 33 (2007)
1686-1693.
[16] R. Gains, J. Mawhin, Coincidence degree and nonlinear differential
equations, Springer-Verlag, Berlin, 1977.
[17] H. Tokumarn, N. Adachi, T. Amemiya, Macroscopic stability of interconnected
systems, 6th IFAC Congress, paper ID44.4, 1975, 1-7.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59560", author = "Daiming Wang", title = "Existence and Global Exponential Stability of Periodic Solutions of Cellular Neural Networks with Distributed Delays and Impulses on Time Scales", abstract = "In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.
", keywords = "Periodic solutions, global exponential stability, coincidence degree, M-matrix.", volume = "5", number = "12", pages = "2038-6", }
