Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying and continuously distributed delays

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 6, 2010, Pages 1655-1663

  Fan, Qiyi ^a   Shao, Jianying ^b  

^a HUNAN UNIVERSITY OF ARTS AND SCIENCE   (China)

^b JIAXING UNIVERSITY   (China)

Author keywords

Almost periodic solution; Continuously distributed delays; Exponential stability; Shunting inhibitory cellular neural networks; Time varying delays

Indexed keywords

ASYMPTOTIC STABILITY; CELLULAR NEURAL NETWORKS; TIME DELAY;

ALMOST PERIODIC SOLUTIONS; CONDITION; CONTINUOUSLY DISTRIBUTED DELAYS; POSITIVE ALMOST PERIODIC SOLUTIONS; SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS; TIME VARYING; TIME-VARYING DELAY;

TIME VARYING NETWORKS;

EID: 72049115505     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.06.026     Document Type: Article

References (20)

1. Bouzerdoum A., and Pinter R.B. Shunting Inhibitory Cellular Neural Networks: Derivation and Stability Analysis. IEEE Trans Circuits Syst 1-Fundam Theor Appl 40 (1993) 215-221
2. Bouzerdoum A., and Pinter R.B. Analysis and analog implementation of directionally sensitive shunting inhibitory cellular neural networks. Visual information processing: from neurons to chips SPIE-1473 (1991) 29-38
3. Bouzerdoum A, Pinter RB. Nonlinear lateral inhibition applied to motion detection in the fly visual system. In: Pinter RB, Nabet B, editors. Nonlinear vision. Boca Raton: FL CRC Press; 1992. p. 423-50.
4. Chen A., Cao J., and Huang L. Almost periodic solution of shunting inhibitory CNNs with delays. Phys Lett A 298 (2002) 161-170
5. Chen A., and Huang X. Almost periodic attractor of delayed neural networks with variable coefficients. Phys Lett A 340 1-4 (2005) 104-120
6. Fink, AM. Almost periodic differential equations, lecture notes in mathematics, vol. 377. Berlin: Springer; 1974.
7. He C.Y. Almost periodic differential equation (1992), Higher Education Publishing House, Beijing [in Chinese]
8. Huang X., and Cao J. Almost periodic solutions of inhibitory cellular neural networks with time-vary delays. Phys Lett A 314 (2003) 222-231
9. Li Y., Liu C., and Zhu L. Global exponential stability of periodic solution of shunting inhibitory CNNs with delays. Phys Lett A 337 (2005) 46-54
10. Liu B., and Huang L. Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Phys Lett A 349 (2006) 177-186
11. Lu W., and Chen T. Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A Math 8 48 (2005) 1015-1026
12. Teng Z. Nonautonomous Lotka-Volterra systems with delays. J Differential Equations 179 2 (2002) 538-561
13. Teng Z. On the positive almost periodic solutions of a class of Lotka-Volterra type systems with delays. J Math Anal Appl 249 2 (2000) 433-444
14. Xu J., and Ho Daniel W.C. Existence and attractivity of almost periodic solution for recurrent neural networks with unbounded delays and variable coefficients. Nonlinear Dyn 45 3-4 (2006) 337-351
15. Xu B., and Yuan R. The existence of positive almost periodic type solutions for some neutral nonlinear integral equation. Nonlinear Anal 60 4 (2005) 669-684
16. Liu B., and Huang L. Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 9 3 (2008) 830-841
17. Cai M., Zhang H., and Yuan Z. Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays. Math Comput Simul 78 4 (2008) 548-558
18. De la Sen M. On positivity of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate point delays. Appl Math Comput 190 1 (2007) 382-401
19. Zhang H., and Li Y.K. Existence of positive periodic solutions for functional equations with impulse effects on time scales. Commun Nonlinear Sci Numer Simul 14 1 (2009) 19-26
20. El-Shahed M. Positive solutions for nonlinear singular third order boundary value problem. Commun Nonlinear Sci Numer Simul 14 2 (2009) 424-429