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Global bifurcation structure of positive stationary solutions for a classical Lotka-Volterra competition model with diffusion

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Abstract

In this paper, we consider a classical Lotka-Volterra competition model with diffusion, and show that the global bifurcation structure of positive stationary solutions for the model is similar to that for a certain scalar reaction-diffusion equation. To do this, the comparison principle, the bifurcation theory and the interval arithmetic are employed.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Ehime University, 790-8577, Matsuyama, Japan

    Yukio Kan-on

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  1. Yukio Kan-on
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Correspondence to Yukio Kan-on.

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Kan-on, Y. Global bifurcation structure of positive stationary solutions for a classical Lotka-Volterra competition model with diffusion. Japan J. Indust. Appl. Math. 20, 285–310 (2003). https://doi.org/10.1007/BF03167424

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  • DOI: https://doi.org/10.1007/BF03167424

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