Boundedness, periodic solutions and global stability for cellular neural networks with variable coefficients and infinite delays

Neurocomputing

Volumn 72, Issue 10-12, 2009, Pages 2455-2463

  Jiang, Haijun ^a   Teng, Zhidong ^a  

^a XINJIANG UNIVERSITY   (China)

Author keywords

Banach space Cg (R ); Boundedness; Cellular neural networks; Globally asymptotic stability; Globally exponential stability; Infinite delays; Lyapunov functional; Periodic solution; Variable coefficients

Indexed keywords

BOUNDEDNESS; GLOBALLY ASYMPTOTIC STABILITY; GLOBALLY EXPONENTIAL STABILITY; INFINITE DELAYS; LYAPUNOV FUNCTIONAL; PERIODIC SOLUTION; VARIABLE COEFFICIENTS;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; BANACH SPACES; DIFFERENTIAL EQUATIONS; PHASE SPACE METHODS; STABILITY CRITERIA; TOPOLOGY;

CELLULAR NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; ASSOCIATIVE MEMORY; CONTROLLED STUDY; INFORMATION PROCESSING; INFORMATION SYSTEM; MATHEMATICAL COMPUTING; NONLINEAR SYSTEM; PRIORITY JOURNAL;

EID: 67349136305     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2008.11.010     Document Type: Article

References (44)

1. Burton T.A. Stability and Periodic Solutions of Ordinary and Functional Differential Equations (1985), Academic Press Inc, New York
2. Burton T.A., and Grimmer R.C. Oscillation, continuation and uniqueness of solutions of retarded differential equations. Trans. Am. Math. Soc. 179 (1973) 193-209
3. Burton T.A., and Zhang S. Uniform bounded, periodicity, and stability in ordinary and functional differential equations. Ann. Math. Pure Appl. 145 (1986) 129-158
4. Cao J., and Liang J. Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. J. Math. Anal. Appl. 296 (2004) 665-685
5. Cao J., and Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. I 50 (2003) 34-44
6. Cao J., and Wang L. Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. Neural Networks 13 (2002) 457-463
7. Chen A. Global stability of neural networks with distributed delays. Neural Networks 15 (2002) 867-871
8. Chen A., and Cao J. Existence and attractive of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients. Appl. Math. Comput. 134 (2003) 125-140
9. Chen A., Huang L., and Cao J. Existence and stability of almost periodic solution for BAM neural networks with delays. Appl. Math. Comput. 137 (2003) 177-193
10. Chen Y. Global stability of neural networks with distributed delays. Neural Networks 15 (2002) 867-871
11. Dong M. Global exponential stability and existence of periodic solutions of CNNs with delays. Phys. Lett. A 300 (2002) 49-57
12. Dong Q., Matsui K., and Huang X. Existence and stability of periodic solutions for Hopfield neural network equations with periodic input. Nonlinear Anal. 49 (2002) 471-479
13. Forti M., and Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problem. IEEE Trans. Circuits Syst. I 42 (1995) 354-366
14. Gopalsamy K., and He X. Delay-independent stability in bidirectional associative memory networks. IEEE Trans. Neural Networks 5 (1994) 998-1002
15. Gopalsamy K., and He X. Stability in asymmetric Hopfield nets with transmission delays. Physica D 76 (1994) 344-358
16. Guo S., Huang L., Dai B., and Zhang Z. Global existence of periodic solutions of BAM neural networks with variable coefficients. Phys. Lett. A 317 (2003) 97-106
17. Hering R.H. Boundedness and periodic solutions in infinite delay system. J. Math. Anal. Appl. 163 (1992) 527-535
18. Huang H., Cao J., and Wang J. Global exponential stability and periodic solutions of recurrent neural networks with delays. Phys. Lett. A 298 (2002) 393-404
19. Huang H., Ho D.W.C., and Cao J. Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays. Neural Networks 18 (2005) 161-170
20. Jiang H., Li Z., and Teng Z. Boundedness and stability for nonautonomous cellular neural networks with delay. Phys. Lett. A 306 (2003) 313-325
21. Jiang H., and Teng Z. Global exponential stability of cellular neural networks with time-varying coefficients and delays. Neural Networks 17 (2004) 1415-1425
22. Joy M. On the global convergence of a class of functional differential equations with applications in neural networks theory. J. Math. Anal. Appl. 232 (1999) 61-81
23. Li Y. Existence and stability of periodic solution for BAM neural networks with distributed delays. Appl. Math. Comput. 159 (2004) 847-862
24. Liang J., and Cao J. Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays. Phys. Lett. A 318 (2003) 53-64
25. Liang J., and Cao J. Global asymptotic stability of bidirectional associative memory networks with distributed delays. Appl. Math. Comput. 152 (2004) 415-424
26. Liao X., Wong K., and Li C. Global exponential stability for a class of generalized neural networks with distributed delays. Nonlinear Anal. Real World Appl. 5 (2004) 527-547
27. Liu Z., Chen A., Cao J., and Huang L. Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays. Phys. Lett. A 319 (2003) 305-316
28. Liu Z., and Liao L. Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays. J. Math. Anal. Appl. 290 (2004) 247-262
29. Makay G. Periodic solutions of linear differential and integral equations. Differential Integral Equations 8 (1995) 2177-2187
30. Makay G. Periodic solutions of dissipative functional differential equations with infinite delay. Tohoku J. Math. 48 (1996) 355-362
31. Mohamad S. Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks. Physica D 159 (2001) 233-251
32. Mohamad S., and Gopalsamy K. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Appl. Math. Comput. 135 (2003) 17-38
33. Peng J., Qiao H., and Xu Z. A new approach to stability of neural networks with time-varying delays. Neural Networks 15 (2002) 95-103
34. Song Q.K. Stability analysis of impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays. Int. J. Neural Syst. 17 (2007) 407-417
35. Song Q.K. Robust stability in Cohen-Grossberg neural network with time-varying and distributed delays. Neural Process Lett. 27 (2008) 179-196
36. Sun J., and Wan L. Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays. Physica D 208 (2005) 1-20
37. Wang L. Stabilizing Hopfield neural networks via inhibitory self-connections. J. Math. Anal. Appl. 292 (2004) 135-147
38. Yang X., Liao X., Megson G.M., and Evans D.J. Global exponential periodicity of a class of neural networks with recent-history distributed delays. Chaos Solitons Fractals 25 (2005) 441-447
39. Zhang B. Boundedness in functional differential equations. Nonlinear Anal. 22 (1994) 1511-1527
40. Zhang Q., Wei X., and Xu J. Global exponential stability of Hopfield neural networks with continuously distributed delays. Phys. Lett. A 315 (2003) 431-436
41. Zhang Y., Pheng H.A., and Leung K.S. Convergence analysis of cellular neural networks with unbounded delay. IEEE Trans. Circuits Syst. I 48 (2001) 680-687
42. Zhao H. Global stability of bidirectional associative memory neural networks with distributed delays. Phys. Lett. A 297 (2002) 182-190
43. Zhao H. Global asymptotic stability of Hopfield neural networks involving distributed delays. Neural Networks 17 (2004) 47-53
44. Zhou J., Liu Z., and Chen G. Dynamics of periodic delayed neural networks. Neural Networks 17 (2004) 87-101