Fixed points and exponential stability for a stochastic neutral cellular neural network

Chengjun Guo; Donald O'Regan; Feiqi Deng; Ravi P. Agarwal

doi:10.13025/28526

Fixed points and exponential stability for a stochastic neutral cellular neural network

Chengjun Guo
, Donald O'Regan
, Feiqi Deng
, Ravi P. Agarwal

Mathematics

Guangdong University of Technology
South China University of Technology
Texas A&M University-Kingsville
King Fahd University of Petroleum and Minerals

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

26 Citations (Scopus)

Abstract

In this paper we study the stability of a stochastic neutral cellular neural network d[x(t)-cx(t-^τ1)]=[-(A+bigtriangleup;A(t))x(t)+f(t, x(t),x(t-^τ2))]dt+σ(t,x(t),x(t-^τ3))dw(t). By using fixed point theory and some analysis techniques, we obtain new criteria for exponential stability in mean square of the considered stochastic neutral cellular neural network. Finally, an example is provided to illustrate the relevance of the results.

Original language	English
Pages (from-to)	849-853
Number of pages	5
Journal	Applied Mathematics Letters
Volume	26
Issue number	8
DOIs	https://doi.org/10.13025/28526 https://doi.org/10.1016/j.aml.2013.03.011
Publication status	Published - Aug 2013

Keywords

Cellular neural network
delays
Exponentially stable
Fixed point theory

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10.13025/28526Licence: CC BY
10.1016/j.aml.2013.03.011

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title = "Fixed points and exponential stability for a stochastic neutral cellular neural network",

abstract = "In this paper we study the stability of a stochastic neutral cellular neural network d[x(t)-cx(t-τ1)]=[-(A+bigtriangleup;A(t))x(t)+f(t, x(t),x(t-τ2))]dt+σ(t,x(t),x(t-τ3))dw(t). By using fixed point theory and some analysis techniques, we obtain new criteria for exponential stability in mean square of the considered stochastic neutral cellular neural network. Finally, an example is provided to illustrate the relevance of the results.",

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T1 - Fixed points and exponential stability for a stochastic neutral cellular neural network

AU - Guo, Chengjun

AU - O'Regan, Donald

AU - Deng, Feiqi

AU - Agarwal, Ravi P.

PY - 2013/8

Y1 - 2013/8

N2 - In this paper we study the stability of a stochastic neutral cellular neural network d[x(t)-cx(t-τ1)]=[-(A+bigtriangleup;A(t))x(t)+f(t, x(t),x(t-τ2))]dt+σ(t,x(t),x(t-τ3))dw(t). By using fixed point theory and some analysis techniques, we obtain new criteria for exponential stability in mean square of the considered stochastic neutral cellular neural network. Finally, an example is provided to illustrate the relevance of the results.

AB - In this paper we study the stability of a stochastic neutral cellular neural network d[x(t)-cx(t-τ1)]=[-(A+bigtriangleup;A(t))x(t)+f(t, x(t),x(t-τ2))]dt+σ(t,x(t),x(t-τ3))dw(t). By using fixed point theory and some analysis techniques, we obtain new criteria for exponential stability in mean square of the considered stochastic neutral cellular neural network. Finally, an example is provided to illustrate the relevance of the results.

KW - Cellular neural network

KW - delays

KW - Exponentially stable

KW - Fixed point theory

UR - http://hdl.handle.net/10379/11761

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VL - 26

SP - 849

EP - 853

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 8

ER -

Fixed points and exponential stability for a stochastic neutral cellular neural network

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Keywords

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