Kirkilionis, Markus A.; Diekmann, Odo; Lisser, Bert; Nool, Margreet; Sommeijer, Ben; de Roos, Andre M. Numerical continuation of equilibria of physiologically structured population models. I: Theory. (English) Zbl 1013.92036 Math. Models Methods Appl. Sci. 11, No. 6, 1101-1127 (2001). Summary: The paper introduces a new numerical method for continuation of equilibria of models describing physiologically structured populations. To describe such populations, we use integral equations coupled with each other via interaction (or feedback) variables. Additionally, we allow interactions with unstructured populations, described by ordinary differential equations. The interaction variables are chosen such that if they are given functions of time, each of the resulting decoupled equations becomes linear. Our numerical procedure to approximate an equilibrium will use this special form of the underlying equations extensively. We also establish a method for local stability analysis of equilibria in dependence on parameters. Cited in 16 Documents MSC: 92D25 Population dynamics (general) 65P99 Numerical problems in dynamical systems 92D40 Ecology 45J05 Integro-ordinary differential equations Keywords:numerical continuation of equilibria Software:PSPManalysis PDFBibTeX XMLCite \textit{M. A. Kirkilionis} et al., Math. Models Methods Appl. Sci. 11, No. 6, 1101--1127 (2001; Zbl 1013.92036) Full Text: DOI References: [1] Saldaa J., J. Math. Biol. 33 pp 335– (1995) [2] DOI: 10.1007/s002850050104 · Zbl 0909.92023 · doi:10.1007/s002850050104 [3] DOI: 10.1007/BF00250793 · Zbl 0286.92005 · doi:10.1007/BF00250793 [4] DOI: 10.1016/0898-1221(90)90267-N · Zbl 0695.92012 · doi:10.1016/0898-1221(90)90267-N [5] DOI: 10.1007/BF00173266 · Zbl 0795.92022 · doi:10.1007/BF00173266 [6] DOI: 10.1016/0022-5193(83)90242-4 · doi:10.1016/0022-5193(83)90242-4 [7] DOI: 10.1016/S0022-5193(75)80126-3 · doi:10.1016/S0022-5193(75)80126-3 [8] DOI: 10.1002/num.1690040303 · Zbl 0658.92016 · doi:10.1002/num.1690040303 [9] DOI: 10.1007/BF00168048 · Zbl 0777.92016 · doi:10.1007/BF00168048 [10] DOI: 10.1007/BF00160170 · Zbl 0796.92022 · doi:10.1007/BF00160170 [11] DOI: 10.1137/0148032 · Zbl 0657.92011 · doi:10.1137/0148032 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.