### Electronic Research Archive

2021, Issue 2: 2187-2221. doi: 10.3934/era.2020112
Special Issues

# Pullback attractors for stochastic recurrent neural networks with discrete and distributed delays

• Received: 01 April 2020 Revised: 01 August 2020 Published: 19 October 2020
• Primary: 34A33; Secondary: 34D45, 34F05

• In this paper, we investigate a class of stochastic recurrent neural networks with discrete and distributed delays for both biological and mathematical interests. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth conditions so that the uniqueness of the Cauchy problem fails to be true. Moreover, the existence of pullback attractors with or without periodicity is presented for the multi-valued noncompact random dynamical system. In particular, a new method for checking the asymptotical compactness of solutions to the class of nonautonomous stochastic lattice systems with infinite delay is used.

Citation: Meiyu Sui, Yejuan Wang, Peter E. Kloeden. Pullback attractors for stochastic recurrent neural networks with discrete and distributed delays[J]. Electronic Research Archive, 2021, 29(2): 2187-2221. doi: 10.3934/era.2020112

### Related Papers:

• In this paper, we investigate a class of stochastic recurrent neural networks with discrete and distributed delays for both biological and mathematical interests. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth conditions so that the uniqueness of the Cauchy problem fails to be true. Moreover, the existence of pullback attractors with or without periodicity is presented for the multi-valued noncompact random dynamical system. In particular, a new method for checking the asymptotical compactness of solutions to the class of nonautonomous stochastic lattice systems with infinite delay is used.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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