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Periodic solutions for a 3x 3 competitive system with cross-diffusion

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  • In this paper we study the role of cross-diffusion in the existence of spatially non-constant periodic solutions for the Lotka-Volterra competition system for three species. By properly choosing cross-diffusion coefficients, we show that Hopf bifurcation occurs at a constant steady state. Furthermore, these spatially nonhomogeneous periodic solutions are stable if diffusion rates are in appropriate ranges.
    Mathematics Subject Classification: Primary: 35K55, 35K57.

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