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Qualitative analysis for a competition model with B‐D functional response and numerical simulation
Author(s) -
Jiang Hongling,
Wu Jianhua,
Wang Lijuan,
Li Jian,
Guo Gaihui
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21848
Subject(s) - uniqueness , mathematics , competition (biology) , fixed point index , stability theory , qualitative analysis , perturbation (astronomy) , competition model , stability (learning theory) , fixed point , mathematical economics , mathematical analysis , computer science , nonlinear system , economics , physics , ecology , quantum mechanics , qualitative research , profit (economics) , social science , machine learning , sociology , microeconomics , biology , boundary value problem
In this article, a competition model with Beddington–DeAngelis functional response is discussed. By the fixed point index theory, some sufficient conditions for the existence of positive solutions are obtained. Moreover, by the regularity theory and perturbation technique, the existence, uniqueness, and stability of positive solutions are established. Our studies show that the competition can be controlled by the intrinsic growth rates and competition coefficients of two species. Especially, one sufficient condition that the system has a unique globally asymptotically stable positive solution is gained. Finally, some numerical simulations are given to support and supplement our theoretical results.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1575–1594, 2014