Weak Mean Random Attractor of Reversible Selkov Lattice Systems Driven By Locally Lipschitz Lévy Noises




Selkov systems, Weak pullback mean random attractor, Lévy noises


This paper is concerned with weak pullback mean random attractor of reversible Selkov lattice systems defined on the entire integer set \(\mathbb{Z}\) driven by locally Lipschitz Lévy noises. Firstly, we formulate the stochastic lattice equations to an abstract system defined in the non-concrete space \(\ell^2\times\ell^2\) of square-summable sequences. Secondly, we establish the global well-posedness of the systems with locally Lipschitz diffusion terms. Under certain conditions, we show that the long-time dynamics can be captured by a weakly compact and weakly attracting mean random attractor in the Bochner space \(L^2(\Omega,\ell^2\times\ell^2)\). To overcome the difficulty caused by the drift and diffusion terms, we adopt a stopping time technique to prove the convergence of solutions in probability. The mean random dynamical systems theory proposed by Wang (J. Differ. Equ., 31:2177-2204, 2019) is used to deal with the difficulty caused by the nonlinear noise.


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2024 Mar 25

How to Cite

G. Li, X. Yang, L. Zhou, and Y. Wang, “Weak Mean Random Attractor of Reversible Selkov Lattice Systems Driven By Locally Lipschitz Lévy Noises”, Electron. J. Appl. Math., vol. 2, no. 1, pp. 40–63, Mar. 2024.



Research Article
Received 2024 Apr 24
Accepted 2024 Apr 29
Published 2024 Mar 25