Positive almost periodic solutions for recurrent neural networks

Nonlinear Analysis: Real World Applications

Volumn 9, Issue 3, 2008, Pages 830-841

  Liu, Bingwen ^a,b   Huang, Lihong ^c  

^a HUNAN UNIVERSITY OF ARTS AND SCIENCE   (China)

^b FUDAN UNIVERSITY   (China)

^c HUNAN UNIVERSITY   (China)

Author keywords

Almost periodic solution; Delays; Exponential stability; Recurrent neural networks

Indexed keywords

ASYMPTOTIC STABILITY; TIME DELAY; TIME VARYING SYSTEMS;

DISTRIBUTED DELAYS; PERIODIC SOLUTIONS;

NEURAL NETWORKS;

EID: 38949119738     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.01.003     Document Type: Article

References (19)

1. Berman A., and Plemmons R.J. Nonnegative Matrices in the Mathematical Science (1979), Academic Press, New York
2. Cao J. Global exponential stability and periodic solutions of delayed cellular neural networks. J. Comput. Syst. Sci. 60 (2000) 38-46
3. Cao J. New results concerning exponential stability and periodic solutions of delayed cellular neural networks with delays. Phys. Lett. A 307 (2003) 136-147
4. 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
5. Cao J., and Song Q. Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19 7 (2006) 1601-1617
6. Cao J., and Wang J. Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans. Circuits Syst.-I 52 5 (2005) 920-931
7. Cao J., and Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst.-I 52 2 (2005) 417-426
8. Chen A., and Cao J. Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients. Appl. Math. Comput. 134 1 (2003) 125-140
9. Chen A., and Huang L.H. Existence and attractivity of almost periodic solutions of Hopfield neutral networks. Math. Acta Scientia 21A 4 (2001) 505-511 (in Chinese)
10. Cheng Z., and Cao J. Bifurcation and stability analysis of a neural network model with distributed delays. Nonlinear Dyn. 45 3-4 (2006) 363-373
11. Dong Q., Matsui K., and Huang X. Existence and stability of periodic solutions for Hopfield neural network equations with periodic input. Nonlinear Anal. 49 (2002) 471-479
12. A.M. Fink, Almost Periodic Differential Equations Lecture Notes in Mathematics, vol. 377, Springer, Berlin, 1974, pp. 80-112.
13. He C. Almost Periodic Differential Equation (1992), Higher Education Publishing House, Beijing, pp. 90-100 (in Chinese)
14. Huang H., Cao J., and Wang J. Global exponential stability and periodic solutions of recurrent cellular neural networks with delays. Phys. Lett. A 298 5-6 (2002) 393-404
15. Huang X., and Cao J. Almost periodic solutions of inhibitory cellular neural networks with time-vary delays. Phys. Lett. A 314 3 (2003) 222-231
16. Liu B., and Huang L. Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Phys. Lett. A 341 (2005) 135-144
17. Liu Z., Chen A., Cao J., and Huang L. Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays. Phys. Lett. A 319 4 (2003) 305-316
18. Liu Z., and Liao L. Existence and global exponential stability of periodic solutions of cellular neural networks with time-vary delays. J. Math. Anal. Appl. 290 2 (2004) 247-262
19. 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