Structure of non-autonomous attractors for a class of diffusively coupled ODE
In this work we will study the structure of the skew-product attractor for a planar diffusively coupled ordinary differential equation, given by $\dot{x}= k(y-x)+x-\beta(t)x^3$ and $\dot{y}= k(x-y)+y-\beta(t)y^3$, $t\geq 0$. We identify the non-autonomous structures that completely describes the dyn...
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| Tipo de documento: | artigo |
| Estado: | Versão preliminar |
| Data de publicação: | 2023 |
| País: | España |
| Recursos: | Universidad de Valladolid |
| Repositório: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:uvadoc.uva.es:10324/69703 |
| Acesso em linha: | https://doi.org/10.3934/dcdsb.2022083 https://uvadoc.uva.es/handle/10324/69703 |
| Access Level: | Acceso aberto |
| Resumo: | In this work we will study the structure of the skew-product attractor for a planar diffusively coupled ordinary differential equation, given by $\dot{x}= k(y-x)+x-\beta(t)x^3$ and $\dot{y}= k(x-y)+y-\beta(t)y^3$, $t\geq 0$. We identify the non-autonomous structures that completely describes the dynamics of this model giving a Morse decomposition for the skew-product attractor. The complexity of the isolated invariant sets in the global attractor of the associated skew-product semigroup is associated to the complexity of the attractor of the associated driving semigroup. In particular, if $\beta$ is asymptotically almost periodic, the isolated invariant sets will be almost periodic hyperbolic global solutions of an associated globally defined problem. |
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