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Nonautonomous bifurcation scenarios in SIR models
Author(s) -
Kloeden P. E.,
Pötzsche C.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3433
Subject(s) - mathematics , bifurcation , simple (philosophy) , stability (learning theory) , eigenvalues and eigenvectors , bifurcation theory , dynamical systems theory , differential equation , mathematical economics , mathematical analysis , nonlinear system , computer science , philosophy , physics , epistemology , quantum mechanics , machine learning
The standard obstacles in developing a bifurcation theory for nonautonomous differential equations are the lack of steady‐state equilibria and the insignificance of eigenvalues in stability investigations. For this reason, various techniques have been proposed to specify changes in the qualitative behavior of time‐dependent dynamical systems. In this paper, we investigate and compare several approaches to nonautonomous bifurcations using SIR‐like models from epidemiology as a paradigm. These models are sufficiently simple to allow explicit solutions to a large extent and consequently enable a detailed discussion of the different results. Copyright © 2015 John Wiley & Sons, Ltd.