Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

Tatra Mountains Mathematical Publications

Volumn 43, Issue 1, 2009, Pages 145-161

  Mohamad, Sannay ^a   Akça, Haydar ^b   Covachev, Valéry ^c  

^a UNIVERSITI BRUNEI DARUSSALAM   (Brunei Darussalam)

^b UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

^c SULTAN QABOOS UNIVERSITY   (Oman)

Author keywords

Cohen Grossberg neural networks; delays; discrete time analogues; Lyapunov exponents

Indexed keywords

EID: 80255134221     PISSN: 12103195     EISSN: None     Source Type: Journal    
DOI: 10.2478/v10127-009-0034-5     Document Type: Article

References (34)

1. AKÇA, H., ALASSAR, R., COVACHEV, V., COVACHEVA, Z.: Discrete counterparts of continuous-time additive Hopfield-type neural networks with impulses, Dynam. Systems Appl. 13 (2004), 77-92.
2. ARIK, S., ORMAN, Z.: Global stability analysis of Cohen-Grossberg neural networks with varying delays, Phys. Lett. A 341 (2005), 410-421.
3. CAO, J., SONG, Q.: Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays, Nonlinearity 19 (2006), 1601-1617.
4. CHEN, Z., RUAN, J.: Global dynamic analysis of general Cohen-Grossberg neural networks with impulse, Chaos Solitons Fractals 32 (2007), 1830-1837.
5. CHEN, Z., RUAN, J.: Global stability analysis of impulsive Cohen-Grossberg neural networks with delay, Phys. Lett. A 345 (2005), 101-111.
6. COHEN, M. A., GROSSBERG, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet. 13 (1983), 815-826.
7. COVACHEV, V., AKÇA, H., COVACHEVA, Z., AL-ZAHRANI, E.: A discrete counterpart of a continuous-time additive Hopfield-type neural networks with impulses in an integral form, Stud. Univ. Žilina Math. Ser. 17 (2003), 11-18.
8. COVACHEV, V., AKÇA, H., YENIÇERIOĞLU, F.: Difference approximations for impulsive differential equations, Appl. Math. Comput. 121 (2001), 383-390.
9. FIEDLER, M.: Special Matrices and Their Applications in Numerical Mathematics, Martinus Nijhoff Publ., Dordrecht, 1986.
10. FORTI, M., TESI, A.: New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans. Circuits Systems I Fund. Theory Appl. 42 (1995), 354-366.
11. GOPALSAMY, K.: Stability of artificial neural networks with impulses, Appl. Math. Comput. 154 (2004), 783-813.
12. HADAMARD, J.-S.: Sur les Correspondences Ponctuelles, OEuvres, Éditions du Centre National de la Recherche Scientifique, Paris, 1968.
13. HORN, R. A., JOHNSON, C. R.: Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
14. HUANG, Z., WANG, X., GAO, F.: The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks, Phys. Lett. A 350 (2006), 182-191.
15. LI, Y.: Existence and exponential stability of periodic solution for continuous-time and discrete-time generalized bidirectional neural networks, Electron. J. Differential Equations 32 (2006), 1-21.
16. LI, Y.: Global exponential stability of BAM neural networks with delays and impulses, Chaos Solitons Fractals 24 (2005), 279-285.
17. LI, Y.: Global stability and existence of periodic solutions of discrete delayed cellular neural networks, Phys. Lett. A 333 (2004), 51-61.
18. LIANG, J., CAO, J.: Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays, Chaos Solitons Fractals 22 (2004), 773-785.
19. LIANG, J., CAO, J., HO, D. W. C.: Discrete-time bidirectional associative memory neural networks with variable delays, Phys. Lett. A 335 (2005), 226-234.
20. LIANG, J., CAO, J., LAM, J. J.: Convergence of discrete-time recurrent neural networks with variable delay, Internat. J. Bif. Chaos Appl. Sci. Engrg. 15 (2005), 581-595.
21. MOHAMAD, S.: Exponential stability preservation in discrete-time analogues of artificial neural networks with distributed delays, J. Comput. Appl. Math. 215 (2008), 270-287.
22. MOHAMAD, S.: Computer simulations of exponentially convergent networks with large impulses, Math. Comput. Simulation 77 (2008), 331-344.
23. MOHAMAD, S.: Global exponential stability in discrete-time analogues of delayed cellular neural networks, J. Difference Equ. Appl. 9 (2003), 559-575.
24. MOHAMAD, S.: Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Phys. D 159 (2001), 233-251.
25. MOHAMAD, S., GOPALSAMY, K.: Dynamics of a class of discrete-time neural networks and their continuous-time counterparts, Math. Comput. Simulation 53 (2000), 1-39.
26. MOHAMAD, S., NAIM, A. G.: Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks, J. Comput. Appl. Math. 138 (2002), 1-20.
27. SONG, Q., CAO, J.: Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays, IEEE Trans. Systems Man Cybernet. Part B 37 (2007), 733-741.
28. SUN, C., FENG, C. B.: Discrete-time analogues of integrodifferential equations modeling neural networks, Phys. Lett. A 334 (2005), 180-191.
29. SUN, C., FENG, C. B.: Exponential periodicity of continuous-time and discrete-time neural networks with delays, Neural Proc. Lett. 19 (2004), 131-146.
30. XIANG, H., YAN, K. M., WANG, B. Y.: Existence and global stability of periodic solution for delayed discrete high-order Hopfield-type neural networks, Discrete Dyn. Nat. Soc. 3 (2005), No. 3, 281-297.
31. YANG, F., ZHANG, C., WU, D.: Global stability of impulsive BAM type Cohen-Grossberg neural networks with delays, Appl. Math. Comput. 186 (2007), 932-940.
32. YANG, Z., XU, D.: Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays, Appl. Math. Comput. 177 (2006), 63-78.
33. ZHANG, J. Y., SUDA, Y., KOMINE, H.: Global exponential stability of Cohen-Grossberg neural networks with variable delays, Phys. Lett. A 338 (2005), 44-50.
34. ZHOU, T., LIU, YUEHUA—LIU, YIRONG: Existence and global exponential stability of periodic solution for discrete-time BAM neural networks, Appl. Math. Comput. 182 (2006), 1341-1354.