Coexistence states and global attractivity for some convective diffusive competing species models

Authors:
Julián López-Gómez and José C. Sabina de Lis

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3797-3833

MSC:
Primary 35Q80; Secondary 34C99, 35K55, 92D25

DOI:
https://doi.org/10.1090/S0002-9947-1995-1311910-8

MathSciNet review:
1311910

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Abstract: In this paper we analyze the dynamics of a general competing species model with diffusion and convection. Regarding the interaction coefficients between the species as continuation parameters, we obtain an almost complete description of the structure and stability of the continuum of coexistence states. We show that any asymptotically stable coexistence state lies in a *global curve of* stable coexistence states and that Hopf bifurcations or secondary bifurcations only may occur from unstable coexistence states. We also characterize whether a semitrivial coexistence state or a coexistence state is a global attractor. The techniques developed in this work can be applied to obtain generic properties of general monotone dynamical systems.

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1311910-8

Article copyright:
© Copyright 1995
American Mathematical Society