Stochastic time-varying competitive neural network systems

Yi Shen; Meiqin Liu; Xiaodong Xu

doi:10.1007/11759966_100

Stochastic time-varying competitive neural network systems

Yi Shen
, Meiqin Liu
, Xiaodong Xu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper we reveal that the environmental noise will suppress a potential population explosion in the stochastic competitive neural network systems with variable delay. To reveal these interesting facts, we stochastically perturb the competitive neural network systems with variable delay ẋ(t) = diag(x₁(t), . . . , x_n(t))[b + Ax(t - δ(t))] into the Itô form dx(t) = diag(x₁(t), . . . , x_n(t))[b + Ax(t - δ(t))]dt + σx(t)dw(t), and show that although the solution to the original delay systems may explode to infinity in a finite time, with probability one that of the associated stochastic delay systems do not.

Original language	English
Title of host publication	Advances in Neural Networks - ISNN 2006
Subtitle of host publication	Third International Symposium on Neural Networks, ISNN 2006, Proceedings
Publisher	Springer Verlag
Pages	683-688
Number of pages	6
ISBN (Print)	354034439X, 9783540344391
DOIs	https://doi.org/10.1007/11759966_100
State	Published - 2006
Externally published	Yes
Event	3rd International Symposium on Neural Networks, ISNN 2006 - Advances in Neural Networks - Chengdu, China Duration: 28 May 2006 → 1 Jun 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3971 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Symposium on Neural Networks, ISNN 2006 - Advances in Neural Networks
Country/Territory	China
City	Chengdu
Period	28/05/06 → 1/06/06

Access to Document

10.1007/11759966_100

Cite this

Shen, Y., Liu, M., & Xu, X. (2006). Stochastic time-varying competitive neural network systems. In Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings (pp. 683-688). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3971 LNCS). Springer Verlag. https://doi.org/10.1007/11759966_100

Shen, Yi ; Liu, Meiqin ; Xu, Xiaodong. / Stochastic time-varying competitive neural network systems. Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Springer Verlag, 2006. pp. 683-688 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{bf48188264a949c8bfb83c99ed620a9f,

title = "Stochastic time-varying competitive neural network systems",

abstract = "In this paper we reveal that the environmental noise will suppress a potential population explosion in the stochastic competitive neural network systems with variable delay. To reveal these interesting facts, we stochastically perturb the competitive neural network systems with variable delay ẋ(t) = diag(x1(t), . . . , xn(t))[b + Ax(t - δ(t))] into the It{\^o} form dx(t) = diag(x1(t), . . . , xn(t))[b + Ax(t - δ(t))]dt + σx(t)dw(t), and show that although the solution to the original delay systems may explode to infinity in a finite time, with probability one that of the associated stochastic delay systems do not.",

author = "Yi Shen and Meiqin Liu and Xiaodong Xu",

year = "2006",

doi = "10.1007/11759966\_100",

language = "英语",

isbn = "354034439X",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "683--688",

booktitle = "Advances in Neural Networks - ISNN 2006",

note = "3rd International Symposium on Neural Networks, ISNN 2006 - Advances in Neural Networks ; Conference date: 28-05-2006 Through 01-06-2006",

}

Shen, Y, Liu, M & Xu, X 2006, Stochastic time-varying competitive neural network systems. in Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3971 LNCS, Springer Verlag, pp. 683-688, 3rd International Symposium on Neural Networks, ISNN 2006 - Advances in Neural Networks, Chengdu, China, 28/05/06. https://doi.org/10.1007/11759966_100

Stochastic time-varying competitive neural network systems. / Shen, Yi; Liu, Meiqin; Xu, Xiaodong.
Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Springer Verlag, 2006. p. 683-688 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3971 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - In this paper we reveal that the environmental noise will suppress a potential population explosion in the stochastic competitive neural network systems with variable delay. To reveal these interesting facts, we stochastically perturb the competitive neural network systems with variable delay ẋ(t) = diag(x1(t), . . . , xn(t))[b + Ax(t - δ(t))] into the Itô form dx(t) = diag(x1(t), . . . , xn(t))[b + Ax(t - δ(t))]dt + σx(t)dw(t), and show that although the solution to the original delay systems may explode to infinity in a finite time, with probability one that of the associated stochastic delay systems do not.

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Shen Y, Liu M, Xu X. Stochastic time-varying competitive neural network systems. In Advances in Neural Networks - ISNN 2006: Third International Symposium on Neural Networks, ISNN 2006, Proceedings. Springer Verlag. 2006. p. 683-688. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11759966_100

Stochastic time-varying competitive neural network systems

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