Open AccessAnalysis of stationary patterns arising from a time-discrete metapopulation model with nonlocal competition
Author(s) -
Ozgur Aydogmus,
Yun Kang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021166
Subject(s) - metapopulation , competition model , competition (biology) , biological dispersal , kernel (algebra) , statistical physics , discrete time and continuous time , nonlinear system , mathematics , discrete space , pattern formation , stability (learning theory) , space (punctuation) , mathematical analysis , pure mathematics , physics , statistics , computer science , ecology , quantum mechanics , biology , economics , population , sociology , genetics , microeconomics , profit (economics) , machine learning , demography , operating system
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.