Dissipativity and periodic attractor for non-autonomous neural networks with time-varying delays

Neurocomputing

Volumn 70, Issue 16-18, 2007, Pages 2953-2958

  Huang, Yumei ^a,b   Xu, Daoyi ^a   Yang, Zhichun ^a  

^a SICHUAN UNIVERSITY   (China)

^b XIHUA UNIVERSITY   (China)

Author keywords

Delay; Differential inequality; Dissipativity; Non autonomous neural networks; Periodic attractor

Indexed keywords

BANACH SPACES; MATRIX ALGEBRA; TIME VARYING SYSTEMS;

DIFFERENTIAL INEQUALITY; DISSIPATIVITY; PERIODIC ATTRACTOR;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; MATHEMATICAL MODEL; PRIORITY JOURNAL; THEORETICAL STUDY;

EID: 34548154789     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2006.10.104     Document Type: Article

References (20)

1. Berman A., and Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences (1979), Academic Press, New York
2. Burton T.A. Stability and Periodic Solutions of Ordinary and Functional Differential Equations (1985), Academic Press, Orlando, Florida
3. Cao J.D. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 307 (2003) 136-147
4. Cao J.D., Yuan K., Ho D.W.C., and Lam J. Global point dissipativity of neural networks with mixed time-varying delays. Chaos 16 (2006) art. no. 013105
5. Gopalsamy K., and He X. Stability in asymmetric Hopfield nets with transmission delays. Physica D 76 (1994) 344-358
6. S. Guo, L. Huang, Stability analysis of a delayed Hopfield neural network, Phys. Rev. E 67 (2003) 061902 1-7.
7. Hale J.K. Theory of Functional Differential Equations (1977), Springer, New York
8. Jiang H.J., Li Zh.M., and Teng Z.D. Boundedness and stability for nonautonomous cellular neural networks with delay. Phys. Lett. A 306 (2003) 313-325
9. Liang J.L., and Cao J.D. Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays. Phys. Lett. A 318 (2003) 53-64
10. Liao X. Mathematical theory of cellular neural networks. Sci. China (Ser. A) 24 (1994) 902-910
11. Mohamad S. Global exponential stability of continuous-time and discrete-time delayed bidirectional neural networks. Physica D 159 (2001) 233-251
12. Rehim M., Jiang H.J., and Teng Z.D. Boundedness and stability for nonautonomous cellular neural networks with delay. Neural Networks 17 (2004) 1017-1025
13. Van DenDriessche P., and Zou X.F. Global attractivity in delayed Hopfield neural networks models. SIAM J. Appl. Math. 58 (1998) 1878-1890
14. Xu D., and Zhao H. Invariant and attracing sets of Hopfield neural networks with delay. Int. J. Syst. Sci. 32 (2001) 863-866
15. Zhang Q., Wei X.P., and Xu J. On global exponential stability of nonautonomous delayed neural networks. Chaos Solitons Fractals 26 (2005) 965-970
16. Zhang Q., Wei X.P., and Xu J. Global exponential stability for nonautonomous cellular neural networks with delays. Phys. Lett. A 351 (2006) 153-160
17. Zhao H. Invariant set and attractor of nonautonomous functional differential systems. J. Math. Anal. Appl. 282 2 (2003) 437-443
18. Zhao H. Global exponential stability and periodicity of cellular neural networks with variable delays. Phys. Lett. A 336 (2005) 331-341
19. Zhao H. Exponential stability and periodic oscillatory of bi-directional associative memory neural network involving delays. Neurocomputing 69 4-6 (2006) 424-448
20. Zeidler E. Nonlinear Functional Analysis and its Application, I: Fixed-Point Theorems (1986), Springer, New York