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Title: Delay driven spatiotemporal chaos in single species population dynamics models
Authors: Petrovskiy, Sergei
Jankovic, Masha
Banerjee, Malay
First Published: 6-May-2016
Publisher: Elsevier on behalf of Academic Press
Citation: Theoretical Population Biology, 2016, 110, pp. 51-62
Abstract: Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can significantly influence population dynamics. In general, time delays may arise from inter- and intra-specific trophic interactions or population structure, however in the context of single species populations they are linked to more intrinsic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two different mathematical formulations. Firstly, we revisit the diffusive logistic equation in which the per capita growth is a function of some specified delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integro-differential model. Using the combination of analytical and numerical techniques, we investigate the effect of time delay on pattern formation. In particular, we show that for sufficiently large values of time delay the system’s dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations.
DOI Link: 10.1016/j.tpb.2016.04.004
ISSN: 0040-5809
eISSN: 1096-0325
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2016. After embargo this will be an open-access article 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.
Appears in Collections:Published Articles, Dept. of Mathematics

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