A numerical approach for investigating the stability of equilibria for structured population models

作者：Breda Dimitri^*; Diekmann Odo; Maset Stefano; Vermiglio Rossana

来源：Journal of Biological Dynamics, 2013, 7: 4-20.

DOI：10.1080/17513758.2013.789562

• numerical equilibrium analysis
• structured populations
• Volterra functional equations
• delay differential equations
• infinitesimal generator

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.

• 出版日期2013