Periodic measures of impulsive stochastic neural networks lattice systems with delays

This paper is concerned with the periodic measures of a class of periodic stochastic neural networks lattice models with delays and nonlinear impulses. First, by employing the idea of uniform estimates on the tails of the solutions, the technique of diadic division, and generalized Ascoli–Arzela the...

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Bibliographic Details
Published in:Journal of mathematical physics 2022-12, Vol.63 (12)
Main Authors: Lin, Yusen, Li, Yayu, Li, Dingshi
Format: Article
Language:English
Subjects:
Krylov-Bogoliubov method
Neural networks
Physics
Tightness
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Summary:This paper is concerned with the periodic measures of a class of periodic stochastic neural networks lattice models with delays and nonlinear impulses. First, by employing the idea of uniform estimates on the tails of the solutions, the technique of diadic division, and generalized Ascoli–Arzela theorem, we prove the tightness of a family of distributions of the segment solutions of the lattice systems. Then, the existence of periodic measures is established by using the Krylov–Bogolyubov method.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0107468