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 x=k(y-x) + x - B(t)x3 and y=k(x-y) + y - B(t)y3, t 0. We identify the non-autonomous structures that completely describes the dynamics of this model giving...

Descripción completa

Detalles Bibliográficos
Autores: Carvalho, Alexandre N., Rocha, Luciano R.N., Langa Rosado, José Antonio, Obaya, Rafael
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:dnet:idus________::27475e6fbf48201f8c0eddec980b7a18
Acceso en línea:https://hdl.handle.net/11441/186683
https://doi.org/10.3934/dcdsb.2022083
Access Level:acceso abierto
Palabra clave:Structure of attractors for non-autonomous dynamical systems
Gradient skew product attractor
Hyperbolic global solutions
Robustness of skew-product attractors under perturbation.
Descripción
Sumario:In this work we will study the structure of the skew-product attractor for a planar diffusively coupled ordinary differential equation, given by x=k(y-x) + x - B(t)x3 and y=k(x-y) + y - B(t)y3, t 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 is asymptotically almost periodic, the isolated invariant sets will be almost periodic hyperbolic global solutions of an associated globally defined problem.