Periodicity and exponential stability of discrete-time neural networks with variable coefficients and delays

Advances in Difference Equations

Volumn 2013, Issue , 2013, Pages

  Xu, Hui ^a,b   Wu, Ranchao ^a  

^a ANHUI UNIVERSITY   (China)

^b Anhui Lvhai Vocational College of Business   (China)

Author keywords

coincidence degree; discrete neural networks; exponential stability; M matrix; periodic solution; variable coefficient

Indexed keywords

EID: 84885647376     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2013-226     Document Type: Article

References (38)

1. Hopfield J: Neurons with graded response have collective computational properties like those of two state neurons. Proc. Natl. Acad. Sci. USA 1984, 81:3088-3092. (Pubitemid 14109528)
2. Chen M, Grossberg S: Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 1983, 13:815-821.
3. Chua L, Yang L: Cellular neural networks: theory and applications. IEEE Trans. Circuits Syst. I 1988, 35:1257-1290.
4. Kosko B: Neural Networks and Fuzzy Systems - A Dynamical System Approach Machine Intelligence. Prentice Hall, Englewood Cliffs; 1992.
5. Hjelmfelt A, Ross J: Pattern recognition, chaos and multiplicity in neural networks and excitable systems. Proc. Natl. Acad. Sci. USA 1994, 91:63-67. (Pubitemid 24018643)
6. Kennedy M, Chua L: Neural networks for nonlinear programming. IEEE Trans. Circuits Syst. 1998, 35:554-562.
7. Cochocki A, Unbehauen R: Neural Networks for Optimization and Signal Processing. Wiley, Stuttgart; 1993.
8. Rolls E, Alessandro T: Neural Networks and Brain Function. Oxford University Press, Oxford; 1998.
9. Marcus CM, Westervelt RM: Stability of analog neural networks with delay. Phys. Rev. A 1989,39(1):347-359.
10. Gopalsamy K, He X: Delay-independent stability in bidirectional associative memory networks. IEEE Trans. Neural Netw. 1994, 5:998-1002.
11. Driessche PV, Zou XF: Global attractivity in delayed Hopfield neural networks. SIAM J. Appl. Math. 1998, 58:1878-1890.
12. Rao V, Phaneendra BR: Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones. Neural Netw. 1999,12(3):455-465. (Pubitemid 29236373)
13. Mohamad S, Gopalsamy K: Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math. Comput. Simul. 2000, 53:1-39.
14. Liu Y, Wang Z, Liu X: Asymptotic stability for neural networks with mixed time-delays: the discrete-time case. Neural Netw. 2009,22(1):67-74.
15. Ensari T, Arik S: New results for robust stability of dynamical neural networks with discrete time delays. Expert Syst. Appl. 2010,37(8):5925-5930.
16. Yu J, Zhang K, Fei S: Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay. Nonlinear Anal., Real World Appl. 2010,11(1):207-216.
17. Alanis AY, Sanchez EN, Loukianov AG, Hernandez EA: Discrete-time recurrent high order neural networks for nonlinear identification. J. Franklin Inst. 2010,347(7):1253-1265.
18. Liu Z, Liao L: Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays. J. Math. Anal. Appl. 2004, 290:247-262. (Pubitemid 38236215)
19. Yucel E, Arik S: New exponential stability results for delayed neural networks with time varying delays. Physica D 2004,191(3-4):314-322.
20. Faydasicok O, Arik S: Robust stability analysis of a class of neural networks with discrete time delays. Neural Netw. 2012, 29-30:52-59.
21. Cheng C, Lin K, Shih C: Multistability and convergence in delayed neural networks. Physica D 2007, 225:61-74. (Pubitemid 44854234)
22. Niculescu SI: Delay Effects on Stability: A Robust Approach. Springer, Berlin; 2001.
23. Stuart A, Humphries A: Dynamical Systems and Numerical Analysis. Cambridge University Press, Cambridge; 1996.
24. Sun C, Feng C: Discrete-time analogues of integrodifferential equations modelling neural networks. Phys. Lett. A 2005, 334:180-191. (Pubitemid 40037420)
25. Mohamad S: Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks. Physica D 2001, 159:233-251. (Pubitemid 33094193)
26. Liang J, Cao JD, Ho D: Discrete-time bidirectional associative memory neural networks with variable delays. Phys. Lett. A 2005, 335:226-234. (Pubitemid 40152956)
27. Liu X, Tang ML, Martin R, Liu BX: Discrete-time BAM neural networks with variable delays. Phys. Lett. A 2007, 367:322-330.
28. Zhao H, Sun L, Wang G: Periodic oscillation of discrete-time bidirectional associative memory neural networks. Neurocomputing 2007, 70:2924-2930. (Pubitemid 47308606)
29. Patan L: Local stability conditions for discrete-time cascade locally recurrent neural networks. Int. J. Appl. Math. Comput. Sci. 2010,20(1):23-34.
30. Gaines RE, Mawhin JL: Coincidence Degree and Nonlinear Differential Equation. Springer, Berlin; 1977.
31. Berman A, Plemmons RJ: Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York; 1979.
32. Chen HC, Hung YC, Chen CK, Liao TL, Chen CK: Image-processing algorithms realized by discrete-time neural networks and their circuit implementations. Chaos Solitons Fractals 2006,29(5):1100-1108.
33. Wang JH: An improved discrete Hopfield neural network for Max-Cut problems. Neurocomputing 2006,69(13-15):1665-1669. (Pubitemid 43906080)
34. Wang JH, Tang Z, Xu XS, Li Y: A discrete competitive Hopfield neural network for cellular channel assignment problems. Neurocomputing 2005, 67:436-442. (Pubitemid 40945740)
35. Yashtini M, Malek A: A discrete-time neural network for solving nonlinear convex problems with hybrid constraints. Appl. Math. Comput. 2008,195(2):576-584. (Pubitemid 350309638)
36. Michele B, Leonarda C, Giuseppe G: Discrete-time cellular neural networks for associate memories with learning and forgetting capabilities. IEEE Trans. Circuits Syst. I 1995,42(7):396-399.
37. Michel AN, Si J, Yen G: Analysis and synthesis of a class of discrete-time neural networks described on hypercubes. IEEE Trans. Neural Netw. 1991,2(1):32-46.
38. McEliece RJ, Posner EC, Rodemich ER, Venkatsch SS: The capacity of the Hopfield associative memory. IEEE Trans. Inf. Theory 1998, 33:461-482.