Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays

Guiling Chen; Dingshi Li; Lin Shi; Onno van Gaans; Sjoerd Verduyn Lunel

doi:10.1016/j.jde.2017.11.032

Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays

Guiling Chen, Dingshi Li, Lin Shi^*, Onno van Gaans, Sjoerd Verduyn Lunel

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays. Our approach is based on the method using fixed point theory, which do not resort to any Liapunov function or Liapunov functional. Our results neither require the boundedness, monotonicity and differentiability of the activation functions nor differentiability of the time varying delays. In particular, a class of neural networks without stochastic perturbations is also considered. Examples are given to illustrate our main results.

Original language	English
Pages (from-to)	3864-3898
Number of pages	35
Journal	Journal of Differential Equations
Volume	264
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2017.11.032
Publication status	Published - 15 Mar 2018

Keywords

Asymptotic stability
Doob's inequality
Exponential stability
Fixed point theory
Stochastic recurrent neural networks
Variable delays

Access to Document

10.1016/j.jde.2017.11.032

1-s2.0-S0022039617306228-mainFinal published version, 671 KBLicence: Taverne

Cite this

@article{8bec62c9f89446c18f6c7a7b76003ef1,

title = "Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays",

abstract = "We present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays. Our approach is based on the method using fixed point theory, which do not resort to any Liapunov function or Liapunov functional. Our results neither require the boundedness, monotonicity and differentiability of the activation functions nor differentiability of the time varying delays. In particular, a class of neural networks without stochastic perturbations is also considered. Examples are given to illustrate our main results.",

keywords = "Asymptotic stability, Doob's inequality, Exponential stability, Fixed point theory, Stochastic recurrent neural networks, Variable delays",

author = "Guiling Chen and Dingshi Li and Lin Shi and {van Gaans}, Onno and {Verduyn Lunel}, Sjoerd",

year = "2018",

month = mar,

day = "15",

doi = "10.1016/j.jde.2017.11.032",

language = "English",

volume = "264",

pages = "3864--3898",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "6",

}

TY - JOUR

T1 - Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays

AU - Chen, Guiling

AU - Li, Dingshi

AU - Shi, Lin

AU - van Gaans, Onno

AU - Verduyn Lunel, Sjoerd

PY - 2018/3/15

Y1 - 2018/3/15

N2 - We present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays. Our approach is based on the method using fixed point theory, which do not resort to any Liapunov function or Liapunov functional. Our results neither require the boundedness, monotonicity and differentiability of the activation functions nor differentiability of the time varying delays. In particular, a class of neural networks without stochastic perturbations is also considered. Examples are given to illustrate our main results.

AB - We present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays. Our approach is based on the method using fixed point theory, which do not resort to any Liapunov function or Liapunov functional. Our results neither require the boundedness, monotonicity and differentiability of the activation functions nor differentiability of the time varying delays. In particular, a class of neural networks without stochastic perturbations is also considered. Examples are given to illustrate our main results.

KW - Asymptotic stability

KW - Doob's inequality

KW - Exponential stability

KW - Fixed point theory

KW - Stochastic recurrent neural networks

KW - Variable delays

UR - http://www.scopus.com/inward/record.url?scp=85039034562&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2017.11.032

DO - 10.1016/j.jde.2017.11.032

M3 - Article

AN - SCOPUS:85039034562

SN - 0022-0396

VL - 264

SP - 3864

EP - 3898

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 6

ER -

Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this