Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses

Chaos, Solitons and Fractals

Volumn 34, Issue 5, 2007, Pages 1599-1607

  Xia, Yonghui ^a   Cao, Jinde ^b   Huang, Zhenkun ^c  

^a FUZHOU UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

^c JIMEI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CELLULAR NEURAL NETWORKS; CHAOS THEORY; FRACTALS;

CONTRACTION PRINCIPLES; SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS (SICNN);

ASYMPTOTIC STABILITY;

EID: 34250211759     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.05.003     Document Type: Article

References (23)

1. Bouzerdoum A., and Pinter R.B. Shunting inhibitory cellular neural networks: derivation and stability analysis. IEEE Trans Circ Syst - I: Fundam Theory Appl 40 3 (1993) 215-221
2. Chen A., and Cao J. Almost periodic solution of shunting inhibitory CNNs with delays. Phys Lett A 298 (2002) 161-170
3. Huang X., and Cao J. Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay. Phys Lett A 314 (2003) 222-231
4. Li Y., Liu C., and Zhu L. Global exponential stability of periodic solution for shunting inhibitory CNNs with delays. Phys Lett A 337 (2005) 40-54
5. Xia YH, Cao J, Lin M. Existence and exponential stability of almost periodic solution for BAM neural networks with impulse, dynamics of continuous, discrete and impulsive systems A, DCDIS proceeding, vol. 3, 2005. p. 248-55.
6. Cao J., Liang J., and Lam J. Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199 3-4 (2004) 425-436
7. Cao J., and Lu J. Adaptive synchronization of neural networks with or without time-varying delays. Chaos 16 (2006) 013133 (6 pages)
8. Cao J., Chen A., and Huang X. Almost periodic attractor of delayed neural networks with variable coefficients. Phys Lett A 340 1-4 (2005) 104-120
9. Bainov D.D., and Simeonov P.S. Theory of impulsive differential equations: periodic solutions and applications (1993), Longman, Harlow
10. Xia Y.H., and Cao J. Almost periodicity in an ecological mode with M-predators and N-preys by "pure-delay tpye" system. Nonlinear Dynam 39 3 (2005) 275-304
11. Lakshmikantham V., Bainov D.D., and Simeonov P. Theory of impulsive differential equations (1989), World Scientific, Singapore
12. Xia YH, Cao J. Almost periodic solutions for an ecological model with infinite delays. Proc Edinburgh Math Soc, in press.
13. Samoilenko A.M., and Perestyuk N.A. Differential equations with impulses effect (1987), Kiev, Visca Skola [in Russian]
14. Liu X., and Ballinger G. Existence and continuability of solutions for differential equations with delays and state-dependent impulses. Nonlinear Anal 51 (2002) 633-647
15. Liu X., and Ballinger G. Uniform asymptotic stability of impulsive delay differential equations. Comput Math Appl 41 (2001) 903-915
16. Yan J.R., Zhao A., and Yan W. Existence and global attractivity of periodic solution for an impulsive delay differential equation with Allee effect. J Math Anal Appl 309 (2005) 489-504
17. Shen J.H. Global existence and uniqueness, oscillation and nonoscillation of impulsive delay differential equations. Acta Math Sinica 40 1 (1997) 53-59 [in Chinese]
18. Yan J.R. Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model. J Math Anal Appl 279 (2003) 111-120
19. Xia YH, Cao J, Lin M. New results on the existence and uniqueness of almost periodic solutions for BAM neural networks with continuously distributed delays. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.10.043.
20. Li Y., Xing W., and Lu L. Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solitons & Fractals 27 (2006) 437-445
21. Cao J., Li P., and Wang W. Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys Lett A 353 4 (2006) 318-325
22. Cao J., and Li X. Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach. Physica D: Nonlinear Phenom 212 1-2 (2005) 54-65
23. Xia YH. Positive periodic solutions for a neutral impulsive delayed Lotka-Volterra competition systems with the effect of toxic substance. Nonlinear Anal: RWA, in press, doi:10.1016/j.nonrwa.2005.07.002.