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dc.contributor.authorde Roos, A.M.
dc.contributor.authorDiekmann, O.
dc.contributor.authorGetto, P.
dc.contributor.authorKirkilionis, M.A.
dc.description.abstractIn this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for "Daphnia consuming algae" models in C-code. The results obtained by way of this implementation are shown in the form of graphs.
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectConsumer resource models
dc.subjectDaphnia models
dc.subjectDelay differential equations
dc.subjectDelay equations
dc.subjectHopf bifurcation
dc.subjectNumerical equilibrium analysis
dc.subjectRenewal equations
dc.subjectStability boundaries
dc.subjectStructured populations
dc.titleNumerical equilibrium analysis for structured consumer resource models
dc.journal.titleBulletin of Mathematical Biologyen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España