Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses

Fuzzy Sets and Systems

Volumn 217, Issue , 2013, Pages 62-79

  Li, Yongkun ^a   Wang, Chao ^a  

^a YUNNAN UNIVERSITY   (China)

Author keywords

Discrete time fuzzy BAM neural networks; Equilibrium point; Global exponential stability; Impulses

Indexed keywords

ANALYTIC METHOD; EQUILIBRIUM POINT; EXPONENTIAL CONVERGENCE RATE; FUZZY BAM NEURAL NETWORKS; GLOBAL EXPONENTIAL STABILITY; IMPULSES; M-MATRIX; NUMERICAL EXAMPLE; SUFFICIENT CONDITIONS; VARIABLE DELAYS;

FUZZY SYSTEMS; TIME VARYING NETWORKS;

NEURAL NETWORKS;

EID: 84873736180     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2012.11.009     Document Type: Article

References (52)

1. J. Hopfield Neural networks and physical systems with emergent collective computational abilities Proc. Natl. Acad. Sci. 79 1982 2554 2558
2. L.O. Chua, and L. Yang Cellular neural networks theory IEEE Trans. Circuits Syst. 35 10 1988 1257 1272
3. M. Cohen, and S. Grossberg Absolute stability of global pattern formation and parallel memory storage by competitive neural networks IEEE Trans. Syst. Man Cybern. 13 5 1983 815 826
4. B. Kosko Bidirectional associative memories IEEE Trans. Syst. Man Cybern. 18 1 1988 49 60
5. N. Dinopoulos A study of the asymptotic behavior of neural networks IEEE Trans. Circuits Syst. 36 1989 863 867
6. K. Urakama Global stability of some class of neural networks Trans. IEICE E 72 1989 863 867
7. A. Denbo, O. Farotimi, and T. Kailath Higher order absolute stable neural networks IEEE Trans. Circuits Syst. 38 1991 57 65
8. S. Koksal, and S. Sivasundaram Stability properties of the Hopfield-type neural networks Dyn. Stability Syst. 8 1993 181 187
9. M. Forti, and A. Tesi New conditions for global stability of neural networks with applications to linear and quadratic programming problems IEEE Trans. Circuits Syst. 42 1995 345 366
10. S. Mohamad, and K. Gopalsamy Dynamics of a class of discrete-time neural networks and their continuous-time counterparts Math. Comput. Simulation 53 2000 1 39
11. Q. Zhu, and X. Li Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks Fuzzy Sets Syst. 203 2012 74 94
12. Q. Zhu, and J. Cao Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays IEEE Trans. Neural Networks Learn. Syst. 23 3 2012 467 479
13. H. Harrer, and J.A. Nossek Discrete-time cellular neural networks Int. J. Circuit Theory Appl. 20 1992 453 467
14. H. Aomori, T. Otake, N. Takahashi, M. Tanaka, Hybrid lifting scheme using discrete-time cellular neural networks for lossless image coding, in: IEEE International Symposium on Circuits and Systems, 2006, pp. 1-4.
15. H. Aomori, K. Kawakami, T. Otake, N. Takahashi, M. Yamauchi, and M. Tanaka Separable 2D lifting using discrete-time cellular neural networks for lossless image coding IEICE Trans. Fundam. E88-A 2005 2067 2614
16. V.M. Brea, D.L. Vilarino, A. Paasio, and D. Cobello Design of the processing core of a mixed-signal CMOS DTCNN chip for pixel-level snakes IEEE Trans. Circuits Syst. I 51 2004 997 1013
17. K. Kayaer, V. Tavsaoglu, A new approach to emulate CNN on FPGAs for real time video processing, in: 11th International Workshop on Cellular Neural Networks and their Applications, Santiago de Compostela, Spain, 2008, pp. 23-28.
18. P. Lopez, D.L. Vilarino, D. Cabello, Design of multilayer discrete time cellular neural networks for image processing tasks based on genetic algorithms, in: IEEE International Symposium on Circuits and Systems, vol. 4, 2000, pp. 133-136.
19. T.J. Su, H. Wang, J. Liu, Particle swarm optimization for image noise cancellation, in: Third International Conference on Intelligent Information, Hiding and Multimedia Signal Processing, 2007, HMSP, vol. 1, 2007, pp. 95-98.
20. N. Takahashi, T. Otake, M. Tanaka, The template optimization of discretetime CNN for image compression and reconstruction, in: IEEE International Symposium on Circuits and Systems, vol. 1, 2002, pp. 237-240.
21. M. Brucoli, L. Carnimeo, and G. Grassi A global approach to the design of discretetime cellular neural networks for associative memories Int. J. Circuit Theory Appl. 24 1996 489 510
22. M. Brucoli, L. Carnimeo, and G. Grassi Discrete-time cellular neural networks for associative memories with learning and forgetting capabilities IEEE Trans. Circuits Syst. I 42 1995 396 399
23. G. Grassi On discrete-time cellular neural networks for associative memories IEEE Trans. Circuits Syst. I 48 2001 107 111
24. G. Grassi On the design of discrete-time cellular neural networks with circulant matrices Int. J. Circuit Theory Appl. 28 2000 193 202
25. E. Kaslik, and S. Sivasundaram Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis Neural Networks 24 2011 370 377
26. S. Arik Global asymptotic stability of bidirectional associative memory neural networks with time delays IEEE Trans. Neural Networks 16 2005 580 586
27. J. Cao, and L. Wang Periodic oscillatory solution of bidirectional associative memory networks Phys. Rev. E 61 2000 1825 1828
28. K. Gopalsamy, and X.Z. He Delay independent stability in bidirectional associative memory networks IEEE Trans. Neural Networks 5 1994 998 1002
29. Z. Huang, and Y. Xia Global exponential stability of BAM neural networks with transmission delays and nonlinear impulses Chaos Solitons Fractals 38 2008 489 498
30. B. Kosko Adaptive bidirectional associative memories Appl. Opt. 26 1987 4947 4960
31. X. Lou, and B. Cui Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays Fuzzy Set Syst. 158 2007 2746 2756
32. S. Senan, and S. Arik Global robust stability of bidirectional associative memory neural networks with multiple time delays IEEE Trans. Syst. Man Cybern. B 37 2007 1375 1381
33. H. Zhao, and N. Ding Dynamic analysis of stochastic bidirectional associative memory neural networks with delays Chaos Solitons Fractals 32 2007 1692 1702
34. B. Zheng, Y. Zhang, and C. Zhang Global existence of periodic solutions on a simplified BAM neural network model with delays Chaos Solitons Fractals 37 2008 1397 1408
35. Z. Zhang, Y. Yang, and Y. Huang Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays Neural Networks 24 2011 457 465
36. Y.K. Li Global exponential stability of BAM neural networks with delays and impulses Chaos Solitons Fractals 24 2005 279 285
37. C. Li, C. Li, X. Liao, and T. Huang Impulsive effects on stability of high-order BAM neural networks with time delays Neurocomputing 74 2011 1541 1550
38. T. Yang, and L. Yang The global stability of fuzzy cellular neural networks IEEE Trans. Circuits Syst. I 43 1996 880 883
39. T. Yang, L. Yang, C.W. Wu, L.O. Chua, Fuzzy cellular neural networks: theory, in: Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications, 1996, pp. 181-186.
40. Y. Liu, and W. Tang Exponential stability of fuzzy cellular neural networks with constant and time-varying delays Phys. Lett. A 323 2004 224 233
41. K. Yuan, J. Cao, and J. Deng Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays Neurocomputing 69 2006 1619 1627
42. T. Huang Exponential stability of delayed fuzzy cellular neural networks with diffusion Chaos Solitons Fractals 31 2007 658 664
43. P. Balasubramaniam, and M. Syed Ali Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays Fuzzy Sets Syst. 161 2010 608 618
44. E. Tian, and C. Peng Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay Fuzzy Sets Syst. 157 2006 544 559
45. X. Lou, and B. Cui Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays Fuzzy Sets Syst. 158 2007 2746 2756
46. R. Rakkiyappan, and P. Balasubramaniam On exponential stability results for fuzzy impulsive neural networks Fuzzy Sets Syst. 161 2010 1823 1835
47. S. Mohamad Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks Physica D 159 2001 233 251
48. S. Mohamad, and K. Gopalsamy Exponential stability of continuous-time and discrete-time cellular neural networks with delays Appl. Math. Comput. 135 2003 17 38
49. J.L. Liang, J.D. Cao, and D.W.C. Ho Discrete-time bidirectional associative memory neural networks with variable delays Phys. Lett. A 335 2005 226 234
50. K.L. Mak, J.G. Peng, Z.B. Xu, and K.F.C. Yiu A new stability criterion for discrete-time neural networks: nonlinear spectral radius Chaos Solitons Fractals 31 2007 424 436
51. Q. Song, and J. Cao Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses J. Franklin Inst. 345 2008 39 59
52. Q. Zhou, and L. Wan Impulsive effects on stability of Cohen-Grossberg-type bidirectional associative memory neural networks with delays Nonlinear Anal. Real World Appl. 10 2009 2531 2540