Periodic solutions for a class of higher-order Cohen-Grossberg type neural networks with delays

Computers and Mathematics with Applications

Volumn 54, Issue 6, 2007, Pages 826-839

  Ren, Fengli ^a   Cao, Jinde ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

Coincidence degree; Delays; Global attractivity; Higher order Cohen Grossberg neural networks; Lyapunov functional; Nonsingular M matrix; Periodic solution

Indexed keywords

LYAPUNOV FUNCTIONS; MATRIX ALGEBRA; PROBLEM SOLVING; THEOREM PROVING;

COINCIDENCE DEGREE; GLOBAL ATTRACTIVITY; HIGHER-ORDER COHEN-GROSSBERG NEURAL NETWORKS; NONSINGULAR M-MATRIX; PERIODIC SOLUTION;

NEURAL NETWORKS;

EID: 34547208733     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.03.005     Document Type: Article

References (31)

1. Cohen M.A., and Grossberg S. Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13 (1983) 815-821
2. Hopfield J.J. Neurons with graded response have collective computational properites like those of two-stage neurons. Proc. Nat. Acad. Sci. USA (Biophysics) 81 (1984) 3088-3092
3. Chua L.O., and Yang L. Cellular neural networks: Theory. IEEE Trans. Circuits Syst. 35 (1988) 1257-1272
4. Wang L., and Zou X. Exponential stability of Cohen-Grossberg neural networks. Neural Netw. 15 (2002) 415-422
5. Ye H., Michel A.N., and Wang K. Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. Phys. Rev. E 51 (1995) 2611-2618
6. Chen T., and Rong L. Delay-independent stability analysis of Cohen-Grossberg neural networks. Phys. Lett. A 317 (2003) 436-449
7. 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
8. Cao J., and Liang J. Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. J. Math. Anal. Appl. 296 (2004) 665-685
9. Wang L., and Zou X. Harmless delays in Cohen-Grossberg neural networks. Physica D 170 (2002) 162-173
10. Wang Z., Liu Y., Li M., and Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 17 3 (2006) 814-820
11. Abu-Mostafa Y., and Jacques J. Information capacity of the Hopfield model. IEEE Trans. Inform. Theory 31 (1985) 461-464
12. McEliece R.J., Posner E.C., Rodemich E.R., and Venkatesh S.S. The capacity of the Hopfield associative memory. IEEE Trans. Inform. Theory 33 (1983) 461-482
13. Baldi P. Neural networks, orientations of the hypercube and algebraic threshold functions. IEEE Trans. Inform. Theory 34 (1998) 523-530
14. Dembo A., Farotimi O., and Kailath T. High-order absolutely stable neural networks. IEEE Trans. Circuits Syst. 38 (1991) 57-65
15. Kosmatopoulos E.B., and Christodoulou M.A. Structural properties of gradient recurrent higher-order neural networks. IEEE Trans. Circuits Syst. II 42 (1995) 592-603
16. Xu B., Liu X., and Liao X. Global asymptotic stability of high-order Hopfield type neural networks with time delays. Comput. Math. Appl. 45 (2003) 1729-1737
17. Cao J., Liang J., and Lam J. Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199 (2004) 425-436
18. 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
19. Ren F., and Cao J. Periodic oscillation of higher-order BAM neural networks with periodic coefficients and delays. Nonlinearity 20 (2007) 605-629
20. Cao J. Periodic oscillation and exponential stability of delayed CNNs. Phys. Lett. A 270 (2000) 157-163
21. Zhou J., Liu Z., and Chen G. Dynamics of periodic delayed neural networks. Neural Netw. 17 (2004) 87-101
22. Cao J., and Wang L. Periodic oscillation solution of bidirectional associative memory networks with delays. Phys. Rev. E 61 (2000) 1825-1828
23. Fu C., He H., and Liao X. Globally stable periodic state of delayed Cohen-Grossberg neural networks. Lecture Notes in Comput. Sci. 3496 (2005) 276
24. Cao J., and Wang J. Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 152 (2005) 920-931
25. Cao J., and Song Q. Stability in Cohen-Grossberg type BAM neural networks with time-varying delays. Nonlinearity 19 (2006) 1601-1617
26. Berman A., and Plemmons R.J. Nonnegative Matrices in the Mathematical Science (1979), Academic Press, New York
27. Chen J., and Chen X. Special Matrices (2001), Tsinghua Univ. Press, Beijing, China pp. 277-299
28. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag, Berlin
29. Gopalsamy K. Stability and Oscillation in Delay Equation of Population Dynamics (1992), Kluwer Acadenic Publishers, Dordreeht
30. Wang Z., Liu Y., Fraser K., and Liu X. Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354 4 (2006) 288-297
31. Wang Z., Shu H., Liu Y., Ho D.W.C., and Liu X. Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos Solitons Fractals 30 4 (2006) 886-896