Numerical Bifurcation Analysis of Physiologically Structured Populations: Consumer-Resource, Cannibalistic and Trophic Models
With the aim of applying numerical methods, we develop a formalism for physiologically structured population models in a new generality that includes con- sumer resource, cannibalism and trophic models. The dynamics at the population level are formulated as a system of Volterra functional equations...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/287 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/287 |
| Access Level: | acceso embargado |
| Palabra clave: | Numerical bifurcation analysis Equilibria Curve continuation Structured populations Consumer-Resource Cannibalism Trophic |
| Sumario: | With the aim of applying numerical methods, we develop a formalism for physiologically structured population models in a new generality that includes con- sumer resource, cannibalism and trophic models. The dynamics at the population level are formulated as a system of Volterra functional equations coupled to ODE. For this general class we develop numerical methods to continue equilibria with respect to a parameter, detect transcritical and saddle-node bifurcations and compute curves in parameter planes along which these bifurcations occur. The methods combine curve continuation, ODE solvers and test functions. Finally we apply the method to the above models using existing data for Daphnia magna consuming Algae, and for Perca fluviatilis feeding on Daphnia magna. In particular we validate the methods by deriving expressions for equilibria and bifurcations with respect to which we compute rrors, and by comparing the obtained curves with curves that were computed earlier with other methods. We also present new curves to show how the methods can easily be applied to derive new biological insight. Schemes of algorithms are included. |
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