Periodic solutions and exponential stability for shunting inhibitory cellular neural networks with continuously distributed delays

Electronic Journal of Differential Equations

Volumn 2008, Issue , 2008, Pages 1-10

  Van Hien, Le ^a   Loan, Tran Thi ^a   Tuan, Duong Anh ^a  

^a HANOI NATIONAL UNIVERSITY OF EDUCATION   (Viet Nam)

Author keywords

Cellular neural networks; Exponential stability; Periodic solutions; Shunting inhibitory; Unbounded delays

Indexed keywords

EID: 38349133318     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. A. Bouzerdoum and R. B. Pinter; Shunting inhibitory cellular neural networks: Derivation and stability analysis, IEEE Transactions on Circuits and Systems: 1-Fundamental Theory and Applications, 40(1993), 215-221.
2. A. Cichocki and R. Unbehauen, Neural networks for Optimization and Signal Processing, Wiley, Chichester, 1993.
3. J. Cao and J. Wang; Global exponential stability and periodicity of recurrent neural networks with time delays, IEEE Trans. on Circuits and Systems -I: Regular paper, 52:5, May, (2005).
4. A. Chen, J. Cao and L. Huang; Periodic solution and global exponential stability for shunting inhibitory delayed cellular neural networks, Electron. J. of Diff. Equations, 2004 (2004), No 29, 1-16.
5. L. O. Chua and L. Yang; Cellular neural network: Application, IEEE.Trans.Circuits Syst., 35:10(1988), 1273-1290.
6. L. O. Chua and L. Yang; Cellular neural network: Theory, IEEE.Trans.Circuits Syst., 35:10(1988), 1257-1272.
7. R. Fengli and J. Cao; Periodic oscillation of higher-order BAM neural networks with periodic coefficients and delays, Nonlinearity, 20:3(2007), 605-629.
8. R. E. Gaines and J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977.
9. H. Jiang, L. Zhang and Zh. Teng; Existence and global exponential stability of almost periodic solution for cellular Neural Networks with variable coefficients and time - varying delays, IEEE Trans. on Neural Networks, 16:6 (2005), 1340-1351.
10. H. Lu, F. Chung and Z. He; Some sufficient conditions for global exponential stability of delayed Hopfield neural networks, Neural networks, 17(2004), 537-544.
11. H. Xia and J. Cao; Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delays, Physic Letter A, 314:3 (2003), 222-231.
12. Y. Xia, J. Cao and H. Zhenkun; Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Chaos, Solitons and Fractals, 34:5 (2007), 1599-1607.
13. K. Yosida, Functional Analysis (sixth edition), Springer-Verlag, Berlin-Heidelberg -New York, 1980.
14. J. Zhang; Absolute stability of a class of neural networks with unbounded delay, Inter.J. of Circuit theory and Appl., 32(2004), 11-21.
15. J. Zhang, Y. Suda and T. Iwasa; Absolutely exponential stability of a class of neural networks with unbounded delay, Neural networks, 17(2004), 391-397.
16. H. Zhao; Global asymptotic stability of Hopfield neural network involving distributed delays, Neural networks, 17(2004), 47-53.
17. Q. Zhou, B. Xiao and Y. Yu; Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays, Electron. J. of Diff. Equations, 2006 (2006), no. 19, 1-10.