Periodic solution to CohenGrossberg BAM neural networks with delays on time scales

Journal of the Franklin Institute

Volumn 348, Issue 10, 2011, Pages 2759-2781

  Zhang, Zhengqiu ^a   Peng, Guoqiang ^a   Zhou, Dongming ^b  

^a HUNAN UNIVERSITY   (China)

^b YUNNAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BAM NEURAL NETWORK; CONTRACTION MAPPING PRINCIPLES; EXISTENCE AND UNIQUENESS; EXISTENCE RESULTS; GLOBAL EXPONENTIAL STABILITY; LYAPUNOV FUNCTIONALS; PERIODIC SOLUTION; TIME-SCALES;

BANACH SPACES; EXPONENTIAL FUNCTIONS; PROBLEM SOLVING; TIME VARYING NETWORKS;

NEURAL NETWORKS;

EID: 80255137583     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2011.08.015     Document Type: Article

References (46)

1. J. Cao, and J. Liang Boundedness and stability of CohenGrossberg neural networks with time-varying delays Journal of Mathematical Analysis and Applications 296 2004 665 685 (Pubitemid 39007492)
2. S. Zhang, C. Li, and X. Liao Global stability of discrete-time CohenGrossberg neural networks with impulses Neurocomputing 73 2010 3132 3138
3. M. Cohen, and S. Grossberg Absolute stability and global pattern formation and parallel memory storage by competitive neural networks IEEE Transactions on Systems Man and Cybernetics 13 1983 815 826
4. Y. Li Existence and stability of periodic solutions for CohenGrossberg neural networks with multiple delays Chaos Solitons Fractals 20 2004 459 466
5. W. Xiong, and J. Cao Global exponential stability of discrete-time CohenGrossberg neural networks Neurocomputing 64 2005 433 446 (Pubitemid 40425331)
6. Q.K. Song, and J.D. Cao Robust stability in CohenGrossberg neural networks with both time-varying and distributed delays Neural Process Letter 27 2008 179 196
7. W.W. Yu, J.D. Cao, and J. Wang An LMI approach to global asymptotic stability of the delayed CohenGrossberg neural network via nonsmooth analysis Neural Networks 20 2007 810 818 (Pubitemid 47361679)
8. S. Mohamad, H. Akca, V. Covachev, Discrete-time CohenGrossberg neural networks with transmission delays and impulses, Tatra Mountains Mathematical Publications 43(2009) 145161.
9. X. Liao, C. Li, and K. Wong Criteria for exponential stability of CohenGrossberg neural networks Neural Networks 17 2004 1401 1414 (Pubitemid 39487137)
10. L.B. Rong, and T.P. Chen New results on the robust stability of Cohen Grossberg neural networks with delays Neural Process Letter 24 3 2006 193 202
11. L. Wang, and X. Zou Harmless delays in CohenGrossberg neural networks Physica D 170 2002 162 173 (Pubitemid 34813927)
12. L. Wang, and X. Zou Exponential stability of CohenGrossberg neural networks Neural Networks 15 2002 415 422 (Pubitemid 34518408)
13. W. Xiong, and J. Cao Global exponential stability of discrete-time CohenGrossberg neural networks Neurocomputing 64 2005 433 446 (Pubitemid 40425331)
14. J. Zhang, Y. Suda, and H. Komine Global exponential stability of CohenGrossberg neural networks with variable delays Physics Letters A 338 2005 44 50 (Pubitemid 40409868)
15. W.L. Lu, and T.P. Chen R n -global stability of a CohenGrossberg neural network system with nonnegative equilibria Neural Networks 20 2007 714 722
16. Z.G. Zeng, J. Wang, Global exponential stability of recurrent networks with time-varying delays in the presence of strong external stimuli, Neural Networks 19 (2006) 15281537. (Pubitemid 44793174)
17. Z.D. Wang, Y.R. Liu, and M. Li Stability analysis for stochastic CohenGrossberg neural networks with mixed time delays IEEE Transactions on Neural Networks 17 3 2006 814 820
18. L. Wang Stability of CohenGrossberg neural networks with distributed delays Applied Mathematics and Computation 160 2005 93 110
19. Z.D. Wang, Y.R. Liu, and X.H. Liu On global asymptotic stability of neural networks with discrete and distributed delays Physics Letters A 345 46 2005 299 308
20. H.Y. Zhao, and L. Wang Hopf bifurcation in CohenGrossberg neural network with distributed delays Nonlinear Analysis: Real World Applications 8 2007 73 89 (Pubitemid 44584785)
21. S. Arik, and Z. Orman Global stability analysis of CohenGrossberg neural networks with time varying delays Physics Letters A 341 2005 410 421 (Pubitemid 40799022)
22. W. Wu, B.T. Cui, and X.Y. Lou Some criteria for asymptotic stability of CohenGrossberg neural networks with time varying delays Neurocomputing 70 2007 1085 1088 (Pubitemid 46043997)
23. Z. Orman, and S. Arik New results for global stability of CohenGrossberg neural networks with multiple time delays Neurocomputing 71 2008 3053 3063
24. B.T. Cui, and W. Wu Global exponential stability of CohenGrossberg neural networks with distributed delays Neurocomputing 72 2008 386 391
25. J. Feng, and S. Xu New criteria on global robust stability of CohenGrossberg neural networks with time varying delays Neurocomputing 72 2008 445 457
26. H.J. Xiang, and J.D. Cao Exponential stability of periodic solution to CohenGrossberg type BAM neural networks with time-varying delay Neurocomputing 72 2009 1702 1711
27. A.P. Chen, and J.D. Cao Periodic bidirectional CohenGrossberg neural networks with distributed delays Nonlinear Analysis 66 2007 2947 2961
28. S. Hilger Analysis on measure chains a unified approach to continuous and discrete calculus Results in Mathematics 18 1990 18 56
29. S. Hilger Differential and difference calculus-unified Nonlinear Analysis 30 1997 2683 2694
30. R.P. Agarwal, M. Bohner, D. ORegan, and A. Peterson Dynamic equations on time scales: a survey Journal of Computational and Applied Mathematics 141 2002 1 26 (Pubitemid 34452340)
31. M. Bohner, and A. Peterson Dynamic Equations on Time Scales: An Introduction with Applications 2001 Birkhauser Boston
32. M. Bohner, and A. Peterson Advances in Dynamic Equations on Time Scales 2003 Birkhaser Boston
33. Y.K. Li, X.R. Chen, and L. Zhao Stability and existence of periodic solutions to delayed CohenGrossberg BAM neural networks with impulses on time scales Neurocomputing 72 2009 1621 1630
34. A.P. Chen, and F.L. Chen Periodic solution to BAM neural network with delays on time scales Neurocomputing 73 2009 274 282
35. M.A. Cohen, and S. Grossberg Absolute stability and global pattern formation and partial memory storage by competitive neural networks IEEE Transactions on Systems Man and Cybernetics 13 1983 815 826
36. B. Kosko Bi-directional associative memories IEEE Transactions on Systems Man and Cybernetics 18 1988 49 60
37. C. Feng, and R. Plamondon Stability analysis of bidirectional associative memory networks with time delays IEEE Transactions on Neural Networks 14 2003 1560 1565
38. K. Gopalsamy, and X. He Delay-independent stability in bidirectional associative memory networks IEEE Transactions on Neural Networks 5 1994 998 1002
39. Z.Q. Zhang, and D.M. Zhou Existence and global exponential stability of a periodic solution for a discrete time interval general BAM neural networks Journal of the Franklin Institute 347 5 2010 763 780
40. X.S. Yang, F. Li, Y. Long, and X.Z. Cui Existence of periodic solution for discrete time cellular neural networks with complex deviating argument and impulses Journal of the Franklin Institute 347 2 2010 559 566
41. R.C. Wu Exponential convergence of BAM neural networks with time-varying coefficients and distributed delays Nonlinear Analysis: Real World Applications 11 2010 562 573
42. H.B. Gu, H.J. Jiang, and Z.D. Teng Existence and global exponential stability of equilibrium of competitive neural networks with differential time scales and multiple delays Journal of the Franklin institute 347 5 2010 719 731
43. A. Tiam, M. Cai, B. Shi, and Q. Zhang Existence and exponential stability of periodic solution for a class of CohenGrossberg BAM neural networks Neurocomputing 73 2010 3147 3159
44. Z. Chen, D.H. Zhao, and X.L. Fu Discrete analogue of high-order periodic CohenGrossberg neural networks with delays Applied Mathematics and Computation 214 2009 210 217
45. Z. Zhang, and L. Wang Existence and global exponential stability of a periodic solution to discrete-time CohenGrossberg BAM neural networks with delays Journal of Korean Mathematics Society 48 4 2011 727 747
46. X. Fu, and Z. Chen New discrete and analogue of neural networks with nonlinear amplification functional and its periodic dynamical analysis, discrete and continuous dynamical system Supplement 2007 391 398