Asymptotic Stabilities of Stochastic Functional Differential Equations

SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(11): 1380-1386

SHEN Yi, JIANG Ming-hui, LIAO Xiao-xin. Asymptotic Stabilities of Stochastic Functional Differential Equations[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1380-1386.

Citation:

SHEN Yi, JIANG Ming-hui, LIAO Xiao-xin. Asymptotic Stabilities of Stochastic Functional Differential Equations[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1380-1386.

Citation:

SHEN Yi, JIANG Ming-hui, LIAO Xiao-xin. Asymptotic Stabilities of Stochastic Functional Differential Equations[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1380-1386.

PDF( 295 KB)

Asymptotic Stabilities of Stochastic Functional Differential Equations

Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

Received Date: 2004-04-03
Rev Recd Date: 2006-08-11
Publish Date: 2006-11-15

Abstract

Abstract

Asymptotic characteristic of the solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Liapunov functions for locating the limit set of the solution.Moreover,from them many effective criteria on stochastic asymptotic stability,which enable us to construct the Liapunov functions much more easily in application were obtained.The results show that the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results.In the end,application in stochastic Hopfield neural networks is given to verify the results.
- stochastic functional differential equation,
- stochastic neural network,
- asymptotic stability,
- semi-martingale convergence theorem,
- It⁰formulsupa

FullText(HTML)

References(12)

References

[1]	黄琳.稳定性与鲁棒性的理论基础[M].北京：科学出版社，2003,45—46.
[2]	Lasalle J P.Stability theory of ordinary differential equations[J].J Differential Equations,1968,4(1):57—65. doi: 10.1016/0022-0396(68)90048-X
[3]	MAO Xue-rong.Some contributions to stochastic asymptotic stability and boundedness via multiple Liapunov functions[J].J Math Anal Appl,2001,260(2)：325—340. doi: 10.1006/jmaa.2001.7451
[4]	MAO Xue-rong.Stochastic versions of the LaSalle-type theorem[J].J Differential Equations,1999,153(1)：175—195. doi: 10.1006/jdeq.1998.3552
[5]	Kolmanovskii V B, Nosov V R.Stability of Functional Differential Equations[M].New York：Academic Press, 1986, 115—120.
[6]	MAO Xue-rong.Stochastic Differential Equations and Applications[M].Chichester：Ellis.Horwood, 1997,158—159.
[7]	沈轶,廖晓昕.非线性随机时滞系统族的鲁棒稳定性[J].自动化学报，1999，25（4）：537—542.
[8]	沈轶,廖晓昕.随机中立型泛函微分方程指数稳定的Razumikhin型定理[J].科学通报,1998，43（21）：2272—2275.
[9]	Hopfield J.Neural networks and physical system with emergent collective computational abilities[J].Proc Nat Acad Sci,USA,1982,79(8):2254—2558.
[10]	Liao X,MAO Xue-rong.Stability of stochastic neural networks[J].Neural,Parallel & Scientific Computations,1996,4(1):205—224.
[11]	沈轶,张玉民,廖晓昕.随机细胞神经网络的指数稳定性[J].电子学报，2002，30（11）：1672—1675.
[12]	Lipster R S, Shiryayev A N.Theory of Martingales[M].Dordrecht: Kluwer Academic, 1989, 201—202.