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Oscillations and Pattern Formation in a Slow-Fast Prey-Predator System.

journal contribution
posted on 12.05.2022, 10:36 by Pranali Roy Chowdhury, Sergei Petrovskii, Malay Banerjee

We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of the prey-predator system is apparent rather than real and there are still many of its hidden properties that have been poorly studied or overlooked altogether. We further focus on the case where, in the slow-fast system, the prey growth is affected by a weak Allee effect. We first consider this system in the non-spatial case and make its comprehensive study using a variety of mathematical techniques. In particular, we show that the interplay between the Allee effect and the existence of multiple timescales may lead to a regime shift where small-amplitude oscillations in the population abundances abruptly change to large-amplitude oscillations. We then consider the spatially explicit slow-fast prey-predator system and reveal the effect of different timescales on the pattern formation. We show that a decrease in the timescale ratio may lead to another regime shift where the spatiotemporal pattern becomes spatially correlated, leading to large-amplitude oscillations in spatially average population densities and potential species extinction.

History

Citation

Bull Math Biol 83, 110 (2021). https://doi.org/10.1007/s11538-021-00941-0

Author affiliation

School of Computing and Mathematical Sciences, University of Leicester

Version

AM (Accepted Manuscript)

Published in

Bull Math Biol

Volume

83

Issue

11

Pagination

110

Publisher

Springer

eissn

1522-9602

Acceptance date

27/08/2021

Copyright date

2021

Available date

17/09/2022

Spatial coverage

United States

Language

eng