title: A numerical approach for investigating the stability of equilibria for structured population models.
abstract: We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems of Volterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved or even unattainable. Therefore, we propose and investigate a numerical method to compute the eigenvalues of the associated infinitesimal generator. The latter is discretized by using a pseudospectral approach, and the eigenvalues of the resulting matrix are the sought approximations. An algorithm is presented to explicitly construct the matrix from the model coefficients and parameters. The method is tested first on academic examples, showing its suitability also for a class of mathematical models much larger than that mentioned above, including neutral- and mixed-type equations. Applications to cannibalism and consumer-resource models are then provided in order to illustrate the efficacy of the proposed technique, especially for studying bifurcations.
authors.affiliation: a Department of Mathematics and Computer Science , University of Udine , via delle Scienze 208, I-33100 Udine , Italy.
authors.forename: Dimitri
authors.initials: D
authors.lastname: Breda
authors.forename: Odo
authors.initials: O
authors.lastname: Diekmann
authors.forename: Stefano
authors.initials: S
authors.lastname: Maset
authors.forename: Rossana
authors.initials: R
authors.lastname: Vermiglio
mesh_terms: D000465:Algorithms; D005502:Food; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical; D011157:Population Dynamics; D040841:Resource Allocation; D013997:Time Factors