Qualitative analysis for a competition model with B-D functional response and numerical simulation

Authors

  • Hongling Jiang,

    1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi, People's Republic of China
    2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, Shaanxi, People's Republic of China
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  • Jianhua Wu,

    Corresponding author
    1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi, People's Republic of China
    • Correspondence to: Jianhua Wu, College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, People's Republic of China, (e-mail: jianhuaw@snnu.edu.cn)

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  • Lijuan Wang,

    1. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, Shaanxi, People's Republic of China
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  • Jian Li,

    1. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, Shaanxi, People's Republic of China
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  • Gaihui Guo

    1. College of Science, Shaanxi University of Science and Technology, Xi'an, Shaanxi, People's Republic of China
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Abstract

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

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