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Title: Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect
Authors: Morozov, A. Y.
Banerjee, M.
Petrovskii, Sergei V.
First Published: 26-Feb-2016
Publisher: Elsevier for Academic Press
Citation: Journal of Theoretical Biology, 2016, 396, pp. 116-124
Abstract: Traditionally, mathematical modeling in population ecology is mainly focused on asymptotic behavior of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct. In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple ‘conceptual’ model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence.
DOI Link: 10.1016/j.jtbi.2016.02.016
ISSN: 0022-5193
eISSN: 1095-8541
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2016. This version of the article is distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License ( ), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description: Following the embargo period the above license applies.
Appears in Collections:Published Articles, Dept. of Mathematics

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