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    Title: Global Dynamics and Traveling Wave Solutions of Two Predators-One Prey Models
    Authors: Lin, Jian-Jhong;Wang, Weiming;Yang, Ting-Hui;Zhao, Caidi
    Contributors: 淡江大學數學學系
    Keywords: Two predators-one prey system;extinction;coexistence;global stability;traveling wave solutions;upper-lower solutions
    Date: 2015-06-01
    Issue Date: 2014-11-27 11:49:15 (UTC+8)
    Publisher: American Institute of Mathematical Sciences
    Abstract: In this work, we consider an ecological system of three species with two predators-one prey type without or with diffusion. For the system without diffusion, i.e. a system of three ODEs, we clarify global dynamics of all equilibria and find an exact condition to guarantee the existence and global asymptotic stability of the positive equilibrium. However, when the corresponding condition does not hold, the prey becomes extinct due to the over exploitation. On the other hand, for the system with diffusion, using the cross iteration method we find the minimum speed c∗. The existence of traveling wave front connecting the trivial solution and the coexistence state with some sufficient conditions is verified if the wave speed is large than c∗ and we also prove the nonexistence of such solutions if the wave speed is less than c∗. Finally, numerical simulations of system without or with diffusion are implemented and biological meanings are discussed.
    Relation: Discrete and Continuous Dynamical Systems-Series B 20(4), pp.1135–1154
    DOI: 10.3934/dcdsb.2015.20.1135
    Appears in Collections:[數學學系暨研究所] 期刊論文

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