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

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 fu...

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Bibliographic Details
Published in:Journal of Differential Equations 2018-03, Vol.264 (6), p.3864-3898
Main Authors: Chen, Guiling, Li, Dingshi, Shi, Lin, van Gaans, Onno, Verduyn Lunel, Sjoerd
Format: Article
Language:English
Subjects:
Asymptotic stability
Doob's inequality
Exponential stability
Fixed point theory
Stochastic recurrent neural networks
Variable delays
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2017.11.032