Numerical bifurcation analysis of a class of nonlinear renewal equations

Show full item record



Permalink

http://hdl.handle.net/10138/208460

Citation

Breda , D , Diekmann , O , Liessi , D & Scarabel , F 2016 , ' Numerical bifurcation analysis of a class of nonlinear renewal equations ' , Electronic Journal of Qualitative Theory of Differential Equations , vol. 2016 , no. 65 , pp. 1-24 . https://doi.org/10.14232/ejqtde.2016.1.65

Title: Numerical bifurcation analysis of a class of nonlinear renewal equations
Author: Breda, Dimitri; Diekmann, Odo; Liessi, Davide; Scarabel, Francesca
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2016-09-12
Language: eng
Number of pages: 24
Belongs to series: Electronic Journal of Qualitative Theory of Differential Equations
ISSN: 1417-3875
URI: http://hdl.handle.net/10138/208460
Abstract: We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic- and Ricker-type population equations and exhibits transcritical, Hopf and period doubling bifurcations. The reliability is demonstrated by comparing the results to those obtained by a reduction to a Hamiltonian Kaplan–Yorke system and to those obtained by direct application of collocation methods (the latter also yield estimates for positive Lyapunov exponents in the chaotic regime). We conclude that the methodology described here works well for a class of delay equations for which currently no tailor-made tools exist (and for which it is doubtful that these will ever be constructed).
Subject: 111 Mathematics
Rights:


Files in this item

Total number of downloads: Loading...

Files Size Format View
p5273.pdf 934.6Kb PDF View/Open

This item appears in the following Collection(s)

Show full item record