Almost periodicity for a class of delayed Cohen-Grossberg neural networks with discontinuous activations

Chaos, Solitons and Fractals

Volumn 45, Issue 9-10, 2012, Pages 1157-1170

  Wang, Jiafu ^a   Huang, Lihong ^b,c  

^a CENTRAL SOUTH UNIVERSITY OF FORESTRY AND TECHNOLOGY   (China)

^b HUNAN UNIVERSITY   (China)

^c HUNAN WOMEN S UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL ACTIVATION;

ALMOST PERIODIC SOLUTIONS; COHEN-GROSSBERG NEURAL NETWORKS; CONSTANT COEFFICIENTS; DELAYED NEURAL NETWORKS; DIFFERENTIAL INCLUSIONS; EXISTENCE AND UNIQUENESS; GLOBAL EXPONENTIAL STABILITY; PERIODIC COEFFICIENTS;

NEURAL NETWORKS;

EID: 84864047305     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2012.05.009     Document Type: Article

References (48)

1. W. Allegretto, D. Papini, and M. Forti Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks IEEE Trans Neural Networ 21 2010 1110 1125
2. J.P. Aubin, and A. Cellina Differential inclusions 1984 Springer Berlin
3. J. Cao Periodic oscillation and exponential stability of delayed CNNs Phys Lett A 270 2000 157 163
4. J. Cao, and T. Chen Globally exponentially robust stability and periodicity of delayed neural networks Chaos Soliton Fract 22 4 2004 957 963
5. J. Cao, and X. Li Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach Physica D 212 2005 54 65 (Pubitemid 41617923)
6. J. Cao, and L. Wang Exponential stability and periodic oscillatory solution in BAM networks with delay IEEE Trans Neural Networ 13 2002 457 463 (Pubitemid 34475046)
7. T. Chen, and L. Rong Delay-independent stability analysis of Cohen-Grossberg neural networks Phys Lett A 317 2003 436 449
8. T. Chen, L. Wang, and C. Ren Existence and global stability analysis of almost periodic solutions for Cohen-Grossberg neural networks Lect Notes Comput Sci 3971 2006 204 210 (Pubitemid 44046109)
9. X. Chen, and Q. Song Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations Neurocomputing 73 2010 3097 3104
10. E.K.P. Chong, S. Hui, and S.H. Zak An analysis of a class of neural networks for solving linear programming problems IEEE Trans Automat Control 44 11 1999 1095 2006
11. L.O. Chua, and L. Yang Cellular neural networks: theory IEEE Trans Circuits Syst I 35 10 1988 1257 1272
12. F.H. Clarke Optimization and nonsmooth analysis 1983 Wiley New York
13. M.A. Cohen, and S. Grossberg Absolute stability and global pattern formation and parallel memory storage by competitive neural networks IEEE Trans Syst Man Cybernet 13 1983 815 826
14. A.F. Filippov Differential equations with discontinuous righthand sides 1988 Kluwer Academic Publishers
15. M. Forti M-matrices and global convergence of discontinuous neural networks Int J Circuits Theor Appl 35 2007 105 130 (Pubitemid 46506957)
16. M. Forti, M. Grazzini, P. Nistri, and L. Pancioni Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations Physica D 214 2006 88 99 (Pubitemid 43131061)
17. M. Forti, and P. Nistri Global convergence of neural networks with discontinuous neuron activations IEEE Trans Circuits Syst I 50 11 2003 1421 1435
18. M. Forti, P. Nistri, and D. Papini Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain IEEE Trans Neural Networ 16 6 2005 1449 1643
19. M. Forti, P. Nistri, and M. Quincampoix Generalized neural network for nonsmooth nonlinear programming problems IEEE Trans Circuits Syst I 51 9 2004 1741 1754
20. G. Haddad Monotone viable trajectories for functional differential inclusions J Differ Equat 42 1981 1 24
21. He X, Lu W, Chen T. Nonnegative periodic dynamics of Cohen-Grossberg neural networks with discontinuous activations and discrete time delays. In: Proc Adv Neural Networ 2009;5551:579-88.
22. D. Hershkowitz Recent directions in matrix stability Linear Algebra Appl 171 1992 161 186
23. M. Hirsch Convergent activation dynamics in continuous time networks Neural Networ 2 1989 331 349 (Pubitemid 20609006)
24. J.J. Hopfield Neurons with graded response have collective computational properties like those of two-state neurons Proc Natl Acad Sci 81 1984 3088 3092 (Pubitemid 14109528)
25. J.J. Hopfield, and D.W. Tank Computing with neural circuits: a model Science 233 1986 625 633 (Pubitemid 16011610)
26. L. Huang, and Z. Guo Global convergence of periodic solution of neural networks with discontinuous activation functions Chaos Soliton Fract 42 2009 2351 2356
27. L. Huang, J. Wang, and X. Zhou Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations Nonlinear Anal Real World Appl 10 2009 1651 1661
28. B.M. Levitan, and V.V. Zhikov Almost periodic functions and differential equations 1982 Cambridge University Press Cambridge
29. L. Li, and L. Huang Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations Appl Math Model 33 2009 4326 4336
30. Y. Li Global exponential stability of BAM neural networks with delays and impulses Chaos Soliton Fract 24 2005 279 285
31. Y. Li, W. Xing, and L. Lu Existence and global exponential stability of periodic solution of a class of neural networks with impulses Chaos Soliton Fractal 27 2006 437 445 (Pubitemid 41037127)
32. X. Liu, and J. Cao On periodic solutions of neural networks via differential inclusions Neural Networ 22 2009 329 334
33. W. Lu, and T. Chen Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions Neural Networ 18 2005 231 242 (Pubitemid 40719525)
34. W. Lu, and T. Chen Dynamical behaviors of delayed neural network systems with discontinuous activation functions Neural Comput 18 2006 683 708 (Pubitemid 43543835)
35. W. Lu, and T. Chen Almost periodic dynamics of a class of delayed neural networks with discontinuous activations Neural Comput 20 4 2008 1065 1090
36. Y. Meng, L. Huang, Z. Guo, and Q. Hu Stability analysis of Cohen-Grossberg neural networks with discontinuous neuron activations Appl Math Model 34 2010 358 365
37. S. Mohamad Exponential stability in Hopfield-type neural networks with impulses Chaos Soliton Fract 32 2007 456 467 (Pubitemid 44559747)
38. D. Papini, and V. Taddei Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations Phys Lett A 343 1-3 2005 117 128 (Pubitemid 40941635)
39. Q. Song, and J. Cao Stability analysis of Cohen-Grossberg neural networks with both time-varying and continuously distributed delays J Comput Appl Math 197 2006 188 203 (Pubitemid 44176249)
40. D.W. Tank, and J.J. Hopfield Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit IEEE Trans Circuits Syst I 33 1986 533 541
41. J. Wang, L. Huang, and Z. Guo Global asymptotic stability of neural networks with discontinuous activations Neural Networ 22 2009 931 937
42. H. Wu Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions Inform Sci 179 2009 3432 3441
43. H. Wu, and C. Shan Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses Appl Math Model 33 2009 2564 2574
44. Y. Xia, J. Cao, and Z. Huang Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses Chaos Soliton Fract 34 2007 1599 1607 (Pubitemid 46907566)
45. Y. Xia, J. Cao, and M. Lin New results on the existence and uniqueness of almost periodic solution for BAM neural networks with continuously distributed delays Chaos Soliton Fract 31 2007 928 936 (Pubitemid 44247664)
46. W. Xiong, Q. Zhou, B. Xiao, and Y. Yu Global exponential stability of cellular neural networks with mixed delays and impulses Chaos Soliton Fract 34 2007 896 902 (Pubitemid 46601903)
47. T. Yoshizawa Stability theory and the existence of periodic solutions and almost periodic solutions 1975 Springer-Verlag Berlin
48. Wang L. Multistability of almost periodic solutions of neural networks with discontinuous activation functions. Third Int. Workshop Adv. Comput. Intell., August 25-27, 2010.