| Texto completo | |
| Autor(es): |
Batko, Bogdan
;
Gameiro, Marcio
;
Hung, Ying
;
Kalies, William
;
Mischaikow, Konstantin
;
Vieira, Ewerton
Número total de Autores: 6
|
| Tipo de documento: | Artigo Científico |
| Fonte: | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 23, n. 1, p. 27-pg., 2024-01-01. |
| Resumo | |
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More precisely, the sparse data is used to construct a statistical surrogate model based on a Gaussian process (GP). The dynamics of the surrogate model is interrogated using combinatorial methods and characterized using algebraic topological invariants (Conley index). The GP predictive distribution provides a lower bound on the confidence that these topological invariants, and hence the characterized dynamics, apply to the unknown dynamical system (assumed to be a sample path of the GP). The focus of this paper is on explaining the ideas, thus we restrict our examples to one-dimensional systems and show how to capture the existence of fixed points, periodic orbits, connecting orbits, bistability, and chaotic dynamics. (AU) | |
| Processo FAPESP: | 19/06249-7 - Aplicações de Métodos Computacionais e Topológicos em Sistemas Dinâmicos |
| Beneficiário: | Marcio Fuzeto Gameiro |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |