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    Title: Existence of traveling wave solutions for diffusive predator–prey type systems
    Authors: Hsu, Cheng-Hsiung;Yang, Chi-Ru;Yang, Ting-Hui;Yang, Tzi-Sheng
    Contributors: 淡江大學數學學系
    Keywords: Traveling wave;Predator–prey;Wazewski Theorem;LaSalleʼs Invariance Principle;Lyapunov function;Hopf bifurcation theory
    Date: 2012-02
    Issue Date: 2012-01-20 02:48:27 (UTC+8)
    Publisher: Maryland Heights: Academic Press
    Abstract: In this work we investigate the existence of traveling wave solutions for a class of diffusive predator–prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalleʼs Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.
    Relation: Journal of Differential Equations 252(4), pp.3040–3075
    DOI: 10.1016/j.jde.2011.11.008
    Appears in Collections:[數學學系暨研究所] 期刊論文

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