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Effect of Slow–Fast Time Scale on Transient Dynamics in a Realistic Prey-Predator System

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posted on 2022-06-24, 10:50 authored by PR Chowdhury, S Petrovskii, M Banerjee
Systems with multiple time scales, often referred to as ‘slow–fast systems’, have been a focus of research for about three decades. Such systems show a variety of interesting, sometimes counter-intuitive dynamical behaviors and are believed to, in many cases, provide a more realistic description of ecological dynamics. In particular, the presence of slow–fast time scales is known to be one of the main mechanisms resulting in long transients—dynamical behavior that mimics a system’s asymptotic regime but only lasts for a finite (albeit very long) time. A prey–predator system where the prey growth rate is much larger than that of the predator is a paradigmatic example of slow–fast systems. In this paper, we provide detailed investigation of a more advanced variant of prey–predator system that has been overlooked in previous studies, that is, where the predator response is ratio-dependent and the predator mortality is nonlinear. We perform a comprehensive analytical study of this system to reveal a sequence of bifurcations that are responsible for the change in the system dynamics from a simple steady state and/or a limit cycle to canards and relaxation oscillations. We then consider how those changes in the system dynamics affect the properties of long transient dynamics. We conclude with a discussion of the ecological implications of our findings, in particular to argue that the changes in the system dynamics in response to an increase of the time scale ratio are counter-intuitive or even paradoxical.

Funding

S.P. was supported by the RUDN University Strategic Academic Leadership Program.

History

Citation

Chowdhury, P.R.; Petrovskii, S.; Banerjee, M. Effect of Slow–Fast Time Scale on Transient Dynamics in a Realistic Prey-Predator System. Mathematics 2022, 10, 699. https://doi.org/10.3390/math10050699

Author affiliation

School of Computing and Mathematical Sciences

Version

  • VoR (Version of Record)

Published in

Mathematics

Volume

10

Issue

5

Pagination

699 - 699

Publisher

MDPI

eissn

2227-7390

Acceptance date

2022-02-21

Copyright date

2022

Available date

2022-02-23

Language

en

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