Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
In this paper, two problems related to FitzHugh-Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise. We obtain a new result ensuring that such a system approximates the cor...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/143019 |
| Acceso en línea: | https://hdl.handle.net/11441/143019 https://doi.org/10.1063/5.0125383 |
| Access Level: | acceso abierto |
| Palabra clave: | Random delay lattice system FitzHugh-Nagumo system Nonlinear Wong-Zakai noise Pullback random attractor Upper semicontinuity |
| Sumario: | In this paper, two problems related to FitzHugh-Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise. We obtain a new result ensuring that such a system approximates the corresponding deterministic system when the correlation time of Wong-Zakai noise goes to infinity rather than to zero. We first prove the existence of tempered random attractors for the random delayed lattice systems with a nonlinear drift function and a nonlinear diffusion term. The pullback asymptotic compactness of solutions is proved thanks to the Ascoli-Arzel`a theorem and uniform tailestimates. We then show that the upper semi-continuous of attractors as the correlation time tends to infinity. As for the second problem, we consider the corresponding deterministic version of the previous model, and study the convergence of attractors when the delay approaches zero. Namely, the upper semicontinuity of attractors for the delayed system to the non-delayed one is proved. |
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