Absolute stability and dynamical stabilisation in predator-prey systems

Ayawoa S. Dagbovie, Jonathan A. Sherratt

Research output: Contribution to journalArticle

Abstract

Many ecological systems exhibit multi-year cycles. In such systems, invasions have a complicated spatiotemporal structure. In particular, it is common for unstable steady states to exist as long-term transients behind the invasion front, a phenomenon known as dynamical stabilisation. We combine absolute stability theory and computation to predict how the width of the stabilised region depends on parameter values. We develop our calculations in the context of a model for a cyclic predator-prey system, in which the invasion front and spatiotemporal oscillations of predators and prey are separated by a region in which the coexistence steady state is dynamically stabilised.

Original languageEnglish
Pages (from-to)1403-1421
Number of pages19
JournalJournal of Mathematical Biology
Volume68
Issue number6
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Absolute stability
  • Ecological invasion
  • Population cycles
  • Vole

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Modelling and Simulation

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