Mean square asymptotic behavior of stochastic neural networks with infinitely distributed delays

Neurocomputing

Volumn 72, Issue 13-15, 2009, Pages 3311-3317

  Li, Bing ^a   Xu, Daoyi ^b  

^a CHONGQING JIAOTONG UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Exponential stability; Halanay inequality; Ito formula; Neural networks; Ultimate boundedness

Indexed keywords

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; NEURAL NETWORKS;

ASYMPTOTIC BEHAVIORS; DIFFERENTIAL INEQUALITY TECHNIQUES; HALANAY INEQUALITY; INFINITELY DISTRIBUTED DELAY; ITO FORMULA; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC NEURAL NETWORK; ULTIMATE BOUNDEDNESS;

STOCHASTIC SYSTEMS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; PROBABILITY;

EID: 77954174536     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2009.01.009     Document Type: Article

References (23)

1. J. Cao, Global asymptotic stability of delayed bi-directional associative memory neural networks, Appl. Math. Comput. 42 (2003) 333-339.
2. J. Cao, New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Phys. Lett. A 307 (2003) 136-147.
3. S. Arik, On the global dissipativity of dynamical neural networks with time delays, Phys. Lett. A 326 (2004) 126-132.
4. Y. Chen, Global stability of neural networks with distributed delays, Neural Networks 15 (2002) 867-871.
5. K. Gopalsamy, X. He, Stability in asymmetric Hopfield nets with transmission delays, Physica D 76 (1994) 344-358.
6. J.J. Hopfield, Neurons with graded response have collective computational properties like those of two-stage neurons, Proc. Natl. Acad. Sci. USA 81 (1984) 3088-3092.
7. S. Haykin, Neural Networks, Prentice-Hall, New Jersey, 1994.
8. X. Liao, J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delays, Phys. Rev. E 68 (2003) 016118 1-7.
9. B. Li, D. Xu, Dissipativity of neural networks with continuously distributed delays, Electron. J. Differential Equations 119 (2006) 1-7.
10. L. Wan, J. Sun, Mean square exponential stability of stochastic delay Hopfield neural networks, Phys. Lett. A 343 (2005) 306-318.
11. D. Xu, Z. Yang, Impulsive delay differential inequality and stability of neural networks, J. Math. Anal. Appl. 305 (2005) 107-120.
12. D. Xu, H. Zhao, Invariant and attracting sets of Hopfield neural networks with delays, Int. J. Syst. Sci. 32 (2001) 863.
13. D. Xu, Asymptotic behavior of Hopfield neural networks with delays, Differential Equations Dyn. Syst. 9 (3) (2001) 353-364.
14. H. Zhao, Global asymptotic stability of Hopfield neural network involving distributed delays, Neural Networks 17 (2004) 47-53.
15. D. Xu, Integro-differential equations and delay integral inequalities, Tôhoku Math. J. 44 (1992) 365.
16. D. Xu, H. Zhao, Invariant set and attractivity of nonlinear differential equations with delays, Appl. Math. Lett. 15 (2002) 321-325.
17. S. Blythe, X. Mao, X. Liao, Stability of stochastic delay neural networks, J. Franklin Inst. 338 (2001) 481-495.
18. Y.H. Xia, J. Cao, Z. Huang, Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Chaos Solitons Fractrals 34 (5) (2007) 1599-1607.
19. Y.H. Xia, J. Cao, M. Lin, New results on the existence and uniqueness of almost periodic solutions for BAM neural networks with continuously distributed delays, Chaos Solitons Fractrals 31 (4) (2007) 928-936.
20. R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
21. J.P. Lasalle, The Stability of Dynamical System, SIAM, Philadelphia, 1976.
22. L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York, 1972.
23. B. Ksendal, Stochastic Differential Equations, sixth ed., Springer, Berlin, 2003.