Gradient Structure of Dynamics for Nonautonomous Cascade Systems
In this paperwe prove the gradient structure of solutions for a nonautonomous cascade system defined on Banach spaces, where the x–variable evolves independently via ˙ x = Ax+ f (t, x) and influences the y–variable through ˙y = By + g(x, y). By first analyzing the long–time dynamics of the nonautono...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2026 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::5708a7248275c887f5252ec31a9dee17 |
| Acesso em linha: | https://hdl.handle.net/11441/186572 https://doi.org/10.1007/s10884-026-10493-3 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Nonautonomous cascade systems Gradient structure Attractors Asymptotic behavior Asymptotically autonomous equations |
| Resumo: | In this paperwe prove the gradient structure of solutions for a nonautonomous cascade system defined on Banach spaces, where the x–variable evolves independently via ˙ x = Ax+ f (t, x) and influences the y–variable through ˙y = By + g(x, y). By first analyzing the long–time dynamics of the nonautonomous x–equation and then examining the resulting y–dynamics for each asymptotic state of x, we provide a complete description of the system’s gradient structure in two levels: a more abstract and general, with less hypotheses on f , and a deeper level of description, when the term f (t, x) is asymptotically autonomous. Finally, we present a descriptionwhen the term f (t, x) is a small nonautonomous perturbation of an autonomous term. |
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