ANALYSIS OF STATIONARY PATTERNS ARISING FROM A TIME-DISCRETE METAPOPULATION MODEL WITH NONLOCAL COMPETITION

Ozgur Aydogmus, Yun Kang

Research output: Contribution to journalArticlepeer-review

Abstract

The paper studies the pattern formation dynamics of a discrete in time and space model with nonlocal resource competition and dispersal. Our model is generalized from the metapopulation model proposed by Doebeli and Killingback [2003. Theor. Popul. Biol. 64, 397-416] in which competition for resources occurs only between neighboring populations. Our study uses symmetric discrete probability kernels to model nonlocal interaction and dispersal. A linear stability analysis of the model shows that solutions to this equation exhibits pattern formation when the dispersal rate is sufficiently small and the discrete interaction kernel satisfies certain conditions. Moreover, a weakly nonlinear analysis is used to approximate stationary patterns arising from the model. Numerical solutions to the model and the approximations obtained through the weakly nonlinear analysis are compared.

Original languageEnglish (US)
Pages (from-to)2917-2934
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume27
Issue number5
DOIs
StatePublished - May 2022

Keywords

  • metapopulation
  • multiscale perturbation
  • Nonlocal coupling
  • pattern formation
  • weakly nonlinear analysis

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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