Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays
Publication date
2018-03-15
Authors
Chen, Guiling
Li, Dingshi
Shi, Lin
van Gaans, Onno
Verduyn Lunel, Sjoerd
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Document Type
Article
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taverne
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, Taverne, Analysis, Applied Mathematics
Citation
Chen, G, Li, D, Shi, L, van Gaans, O & Verduyn Lunel, S 2018, 'Stability results for stochastic delayed recurrent neural networks with discrete and distributed delays', Journal of Differential Equations, vol. 264, no. 6, pp. 3864-3898. https://doi.org/10.1016/j.jde.2017.11.032