Phase-space analysis of large ODE systems using a low-dimensional conservation law
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2015
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911123173801984 |
|---|---|
| author | Budko, Neil V. Vermolen, Fred J. |
| author_facet | Budko, Neil V. Vermolen, Fred J. |
| contents | Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting problems can be formulated as a low-dimensional phase-space conservation law and solved either explicitly or with simple iterative methods. In particular, we consider: non-interacting populations with unbounded and logistic growth, populations with randomized and biased migration, populations competing for a resource, coexisting species, and populations with phase-space interactions. The method provides an alternative to Monte Carlo simulations and may be useful in the fast analysis of biological data and/or removal of deterministic trends. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1503_00922 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Phase-space analysis of large ODE systems using a low-dimensional conservation law Budko, Neil V. Vermolen, Fred J. Dynamical Systems Biological Physics 92D25, 35L03, 35L65 Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting problems can be formulated as a low-dimensional phase-space conservation law and solved either explicitly or with simple iterative methods. In particular, we consider: non-interacting populations with unbounded and logistic growth, populations with randomized and biased migration, populations competing for a resource, coexisting species, and populations with phase-space interactions. The method provides an alternative to Monte Carlo simulations and may be useful in the fast analysis of biological data and/or removal of deterministic trends. |
| title | Phase-space analysis of large ODE systems using a low-dimensional conservation law |
| topic | Dynamical Systems Biological Physics 92D25, 35L03, 35L65 |
| url | https://arxiv.org/abs/1503.00922 |