Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays

Theoretical Computer Science

Volumn 403, Issue 1, 2008, Pages 3-10

  Yang, Zhiguo ^a   Xu, Daoyi ^b  

^a SICHUAN NORMAL UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Attracting set; Delay; Global exponential stability; Invariant set; Non autonomous neural networks; Periodic attractor; Reaction diffusion

Indexed keywords

ADDITION REACTIONS; ARTIFICIAL INTELLIGENCE; DIFFUSION; DIFFUSION IN LIQUIDS; SEMICONDUCTOR DOPING; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS; TIME VARYING SYSTEMS;

(I ,J) CONDITIONS; (PL) PROPERTIES; DIFFUSION OPERATORS; ELSEVIER (CO); EXISTENCE AND UNIQUENESS; GLOBAL DYNAMICAL BEHAVIOR; GLOBAL DYNAMICS; GLOBAL EXPONENTIAL STABILITY (GES); INVARIANT SETS; NON AUTONOMOUS; NOVEL METHODS; REACTION-DIFFUSION (R-D); TIME-VARYING DELAYED;

NEURAL NETWORKS;

EID: 47949092212     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2008.04.044     Document Type: Article

References (21)

1. Zhang Y. Global exponential convergence of recurrent neural networks with variable delays. Theoretical Computer Science 312 (2004) 281-293
2. Lu H.T., Shen R.M., and Chung F.L. Absolute exponential stability of a class of recurrent neural networks with multiple and variable delays. Theoretical Computer Science 344 (2005) 103-119
3. Zhang Q., Wei X., and Xu J. Delay-dependent exponential stability of cellular neural networks with time-varying delays. Chaos, Solitons & Fractals 23 (2005) 1363-1369
4. Liang J., and Cao J. Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays. Chaos, Solitons & Fractals 22 (2004) 773-785
5. Van DenDriessche P., and Zou X.F. Global attractivity in delayed Hopfield neural networks models. SIAM Journal of Applied Mathematics 58 (1998) 1878-1890
6. Xu D.Y., Zhao H.Y., and Zhu H. Global dynamics of Hopfield neural networks involving variable delays. Computers and Mathematics with Applications 42 (2001) 39-45
7. Li X., Huang L., and Zhu H. Global stability of cellular neural networks with constant and variable delays. Nonlinear Analysis 53 (2003) 319-333
8. Zhang Y. Global exponential stability and periodic solutions of delay Hopfield neural networks. International Journal of Systems Science 27 (1996) 227-231
9. Zeng Z.G., and Wang J. Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli. Neural Networks 19 (2006) 1528-1537
10. Forti M., and Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Transactions on Circuits and Systems I 42 (1995) 354-366
11. Zeng Z.G., and Wang J. Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Transactions on Neural Networks 17 (2006) 623-635
12. Xu D.Y., and Zhao H.Y. Invariant and attracing sets of Hopfield neural networks with delay. International Journal of Systems Science 32 (2001) 863-866
13. Mohamad S., and Gopalsamy K. Neuronal dynamics in time varying environments: Continuous and discrete time models. Discrete and Continuous Dynamical Systems 6 (2000) 841-860
14. Jiang H., Li Z., and Teng Z. Boundedness and stability for nonautonomous cellular neural networks with delay. Physics Letters A 306 (2003) 313-325
15. He Q., and Kang L. Existence and stability of global solution for generalized Hopfield neural network system. Neural Parallel & Scientific Computation 2 (1994) 165-176
16. Liao X., Fu Y., Gao J., and Zhao X. Stability of Hopfield neural networks with reaction-diffusition terms. Acta Electron Sinica 28 (2000) 78-80 (in Chinese)
17. Liao X., Yang S., Cheng S., and Zhen Y. Stability of generalized Hopfield neural networks with reaction-diffusition terms. Science in China (Series E) 32 (2002) 87-94 (in Chinese)
18. Wang L.S., and Xu D.Y. Global exponential stability of reaction-diffusion Hopfield neural networks with variable delays. Science in China (Series E) 33 (2003) 488-495 (in Chinese)
19. Wu J. Theory and Application of Partial Functional Differential Equations (1996), Springer-Verlag, New York
20. Liao X. Theory and Application of Stability for Dynamical Systems (2000), Defence Industry Publishing House, BeiJing
21. Zeidler E. Nonlinear Functional Analysis and its Application, I: Fixed-point Theorems (1986), Springer-Verlag, New York