Convergence for a class of delayed recurrent neural networks without M-matrix condition

Journal of Computational and Applied Mathematics

Volumn 233, Issue 2, 2009, Pages 137-141

  Liu, Bingwen ^a   Gong, Shuhua ^a   Yi, Xuejun ^b   Huang, Lihong ^b  

^a JIAXING UNIVERSITY   (China)

^b HUNAN UNIVERSITY   (China)

Author keywords

limit set; Convergence; Delays; M matrix condition; Recurrent neural network model

Indexed keywords

ASYMPTOTIC BEHAVIOR OF SOLUTIONS; CONVERGENCE; DELAYED RECURRENT NEURAL NETWORKS; DELAYS; EQUILIBRIUM POINT; M-MATRIX; M-MATRIX CONDITION; RECURRENT NEURAL NETWORK MODEL;

REINFORCEMENT LEARNING;

RECURRENT NEURAL NETWORKS;

EID: 69249202249     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.07.006     Document Type: Article

References (19)

1. Hopfied J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79 (1982) 2554-2558
2. Hopfied J. Neurons with graded response have collective computational properties like those of two-stage neurons. Proc. Natl. Acad. Sci. USA 81 (1984) 3088-3092
3. Wu J. Introduction to Neural Dynamics and Signal Transmission Delay (2001), Walter de Cruyter, Berlin
4. 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
5. 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
6. 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
7. Liu B., and Huang L. Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal. RWA 9 (2008) 830-841
8. Chen T. Global convergence of delayed dynamical systems. IEEE Trans. Neural Netw. 12 (2001) 1532-1536
9. Chu T. An exponential convergence estimate for analog neural networks with delay. Phys. Lett. A 283 (2001) 113-118
10. Ma W., Saito Y., and Takeuchi Y. M-matrix structure and harmless delays in a hopfield-type neural network. Appl. Math. Lett. (2009) 10.1016/j.aml.2009.01.025
11. Chen L., and Zhao H. New LMI conditions for global exponential stability of cellular neural networks with delays. Nonlinear Anal. RWA 10 (2009) 287-297
12. Cao J., Ho D.W.C., and Huang X. LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay. Nonlinear Anal. 66 (2007) 1558-1572
13. Ren F., and Cao J. LMI-based criteria for stability of high-order neural networks with time-varying delay. Nonlinear Anal. RWA 7 (2006) 967-979
14. Yi T.S., and Huang L.H. Convergence for pseudo monotone semiflows on product ordered topological spaces. J. Differential Equations 214 (2005) 429-456
15. Hale J., and Lunel S.V. Introduction to Functional Differential Equations (1993), Springer-Verlag
16. Yi T.S., and Huang L.H. Asymptotic behavior of solutions to a class of systems of delay differential equations. Acta Math. Sinica 23 8 (2007) 1375-1384
17. Cooke K.L., and Kaplan J.L. A periodicity threshold theorem for epidemic and population growth. Math. Biosci. 31 (1976) 87-104 410-423
18. Cooke K.L., and Yorke J. Some equations modelling growth process and gonorrhea epidemics. Math. Biosci. 16 (1973) 75-107 155-163
19. Györi I. Connections between compartmental systems with pipes and integrodifferential equations. Math. Model. 7 (1986) 1215-1238