Global asymptotic stability for neural network models with distributed delays

Mathematical and Computer Modelling

Volumn 50, Issue 1-2, 2009, Pages 81-91

  Oliveira, José J ^a  

^a UNIVERSITY OF MINHO   (Portugal)

Author keywords

Delayed neural network models; Distributed delays; Global asymptotic stability; M matrix; Time varying delays

Indexed keywords

DELAYED NEURAL NETWORK MODELS; DISTRIBUTED DELAYS; GLOBAL ASYMPTOTIC STABILITY; M-MATRIX; TIME-VARYING DELAYS;

ASSOCIATIVE PROCESSING; ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; NEURAL NETWORKS; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS;

SYSTEM STABILITY;

EID: 67349211767     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2009.02.002     Document Type: Article

References (27)

1. Bélair J. Stability in a model of a delayed neural network. J. Dynam. Differential Equations 5 (1993) 607-623
2. Chen Y. Global asymptotic stability of delayed Cohen-Grossberg neural networks. IEEE Trans. Circuits Syst. 53 (2006) 351-357
3. Van Den Driessche P., and Zou X. Global stability in delayed hopfield neural network models. SIAM J. Appl. Math. 58 (1998) 1878-1890
4. Wu J. Introduction to Neural Dynamics and Signal Transmission Delay (2001), Walter de Gruyter, New York
5. Cohen M., and Grossberg S. Absolute stability, global pattern formation, parallel memory storage bycompetitive neural networks. IEEE Trans. Systems Man Cybern. 13 (1983) 815-826
6. Hopfield J.J. Neural networks with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. 81 (1984) 3088-3092
7. Campbell S.A. Delay independent stability for additive neural networks. Differential Equations Dynam. Systems 9 (2001) 115-138
8. Cao J., and Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. 50 (2003) 34-44
9. Chen T., and Rong L. Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Trans. Neural Netw. 15 (2004) 203-206
10. Huang H., Cao J., and Qu Y. Global robust stability of delayed neural networks with a class of general activation functions. J. Comput. Systems Sci. 69 (2004) 688-700
11. Song Q., and Cao J. Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays. J. Comput. Appl. Math. 197 (2006) 188-203
12. Qiao H., Peng J., Xu Z., and Zhang B. A reference model approach to stability analysis of neural network. IEEE Trans. Systems Man Cybern. 33 (2003) 925-936
13. Wang M., and Wang L. Global asymptotic robust stability of static neural network models with S-type distributed delays. Math. Comput. Modelling 44 (2006) 218-222
14. Kosko B. Bidirectional associative memories. IEEE Trans. Systems Man Cybern. 18 (1988) 49-60
15. Arik S. Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays. IEEE Trans. Neural Netw. 16 (2005) 580-586
16. Cao J., and Song Q. Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19 (2006) 1601-1617
17. Wang L., and Zou X. Hopf bifurcation in bidirectional associative memory neural networks with delays: Analysis and computation. J. Comput. Appl. Math. 167 (2004) 73-90
18. Wang L., and Zou X. Stability and bifurcation of bidirectional associative memory neural networks with delayed self-feedback. Int. J. Bifur. Chaos 15 (2005) 2145-2159
19. Faria T. Asymptotic stability for delayed logistic type equations. Math. Comput. Modelling 43 (2006) 433-445
20. Faria T., and Liz E. Boundedness and asymptotic stability for delayed equations of logistic type. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 1057-1073
21. Faria T., and Oliveira J.J. Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. J. Differential Equations 244 (2008) 1049-1079
22. Fiedler M. Special Matrices and Their Applications in Numerical Mathematics (1986), Martinus Nijhoff Publ. Kluwer, Dordrecht
23. Ozcan N., and Arik S. Global robust stability analysis of neural networks with multiple time delays. IEEE Trans. Circuits Syst. 53 (2006) 166-176
24. Forti M., and Tesi A. New condition for global stability of neural networks with application to linear, quadratic programming problems. IEEE Trans. Circuits Syst. 42 (1995) 354-366
25. Cao J., and Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. 52 (2005) 417-426
26. Li C., Chen J., and Huang T. A new criterion for global robust stability of interval neural networks with discrete time delays. Chaos, Solitons Fractals 31 (2007) 561-570
27. Wang L., and Zou X. Harmless delays in Cohen-Grossberg neural networks. Physica D 170 (2002) 162-173