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Influences of migrations from local competitive pressures on populations between patches

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Abstract

A mathematical model of two competitive populations with migrations between two patches is proposed, which incorporates the dispersals produced by local competitive pressures. It is shown that the density-dependent migrations enhance the persistence of the two competitive populations. Compared with constant migrations, the dispersals from local competitive pressures induce dramatic changes of dynamical behavior of the model. First, the model admits a transition from one stable positive equilibrium to bistable positive equilibria. Second, the model exhibits bifurcations with the existence of seven positive steady states, in which two stable positive equilibria coexist with two stable boundary equilibrium points. These changes alter the distribution of the two populations in the two patches and increase their survival possibilities.

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Authors and Affiliations

  1. Key Laboratory of Eco-environments in Three Gorges Reservoir Region, School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P.R. China

    Xu Zhang & Wendi Wang

  2. Elementary Education College, Chongqing Normal University, Chongqing, 400700, P.R. China

    Xu Zhang

Authors
  1. Xu Zhang
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  2. Wendi Wang
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Correspondence to Wendi Wang.

Additional information

Supported by the National Natural Science Foundation of China (10871162), the Key Project of Chinese Ministry of Education (No. 109132) and Technology Innovation Fund of Postgraduates of Southwest University (KY2009012).

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Zhang, X., Wang, W. Influences of migrations from local competitive pressures on populations between patches. J. Appl. Math. Comput. 37, 313–330 (2011). https://doi.org/10.1007/s12190-010-0436-1

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  • DOI: https://doi.org/10.1007/s12190-010-0436-1

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