Almost periodic solutions of shunting inhibitory cellular neural networks on time scales

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 8, 2012, Pages 3258-3266

  Li, Yongkun ^a   Wang, Chao ^a  

^a YUNNAN UNIVERSITY   (China)

Author keywords

Almost periodic solutions; Asymptotic stability; Shunting inhibitory cellular neural networks; Time scales

Indexed keywords

CELLULAR NEURAL NETWORKS; DIFFERENCE EQUATIONS; TIME MEASUREMENT;

ACTIVATION FUNCTIONS; ALMOST PERIODIC SOLUTIONS; CONDITION; CONTINUOUSLY DISTRIBUTED DELAYS; LIPSCHITZ CONDITIONS; SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS; TIME VARYING; TIME-SCALES;

ASYMPTOTIC STABILITY;

EID: 84857641586     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.11.034     Document Type: Article

References (22)

1. Hilger S, Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg; 1988.
2. Bohner M., Peterson A. Dynamic equations on time scales. An introduction with applications 2001, Birkhäuser Boston, Inc., Boston, MA.
3. Bohner M., Peterson A. Advances in dynamic equations on time scales 2003, Birkhäuser Boston Inc., Boston, Mass, USA.
4. Li Y.K., Shu J. Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun Nonlinear Sci Numer Simulat 2011, 16:3326-3336.
5. Li Y.K., Chen X., Zhao L. Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales. Neurocomputing 2009, 72:21-30.
6. Li Y.K., Zhang T.W. On the existence of solutions for impulsive duffing dynamic equations on time scales with Dirichlet boundary conditions. Abs Appl Anal 2010, 2010. [Article ID 152460, 27 pp.].
7. Li Y.K., Wang C. Almost periodic functions on time scales and applications. Discrete Dynam Nat Soc 2011, 2011. [Article ID 727068, 20 pp.].
8. Castillo S., Pinto M. Asymptotic behavior of functional dynamic equations in time scale. Dynam Syst Appl 2010, 19:165-177.
9. Erbe L., Peterson A., Rehk P. Comparison theorems for linear dynamic equations on time scales. J Math Anal Appl 2002, 275:418-438.
10. Liu H., Xiang X. A class of the first order impulsive dynamic equations on time scales. Nonlinear Anal 2008, 69:2803-2811.
11. Li Y.K., Wang C. Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales. Abs Appl Anal 2011, 2011. [Article ID 341520, 22 pp.].
12. Bouzerdoum A., Pinter R.B. Shunting inhibitory cellular neural networks: derivation and stability analysis. IEEE Trans Circ Syst 1 - Fundam Theory Appl 1993, 40:215-221.
13. Bouzerdoum A, Pinter RB. Analysis and analog implementation of directionally sensitive shunting inhibitory Cellular Neural Networks. In: Visual Information Processing: From Neurons to Chips, vol. SPIE-1473; 1991. p. 29-38.
14. Bouzerdoum A., Pinter R.B. Nonlinear lateral inhibition applied to motion detection in the fly visual system. Nonlinear Vis 1992, 423-450. CRC Press, Boca Raton, FL. R.B. Pinter, B. Nabet (Eds.).
15. Li Y., Liu C., Zhu L. Global exponential stability of periodic solution of shunting inhibitory CNNs with delays. Phys Lett A 2005, (337):46-54.
16. Li Y.K., Zhao L., Liu P. Existence and exponential stability of periodic solution of high-order Hopfield neural network with delays on time scales. Discrete Dynam Nat Soc 2009, 2009. [Article ID 573534, 18 pp.].
17. Li Y., Fan X. Existence and globally exponential stability of almost periodic solution for Cohen-Grossberg BAM neural networks with variable coefficients. Appl Math Model 2009, 33:2114-2120.
18. Fink A.M. Almost periodic differential equation 1974, Springer-Verlag, Berlin, Heidleberg, New York.
19. Teng Z. Nonautonomous Lotka-Volterra systems with delays. J Differ Equ 2002, 179:538-561.
20. Teng Z. On the positive almost periodic solutions of a class of Lotka-Volterra type systems with delays. J Math Anal Appl 2000, 249:433-444.
21. Xu B., Yuan R. The existence of positive almost periodic type solutions for some neutral nonlinear integral equation. Nonlinear Anal 2005, 60:669-684.
22. Liu B., Huang L. Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 2008, 9:830-841.