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Global dynamics of the Lotka–Volterra competition–diffusion system with equal amount of total resources, II

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Abstract

Part II of this series of three papers, we focus on the joint effects of diffusion and spatial concentration on the global dynamics of a classical Lotka–Volterra competition–diffusion system. For comparison purposes, we assume that the two species have identical competition abilities and the same amount of total resources throughout this paper. Part II is devoted to the case that the spatial distribution of resources for one species is heterogeneous while that of the other is homogeneous. Our results imply that in this case not only is the former guaranteed to survive, in fact, it will often wipe out the latter, regardless of initial values. Asymptotic behaviors of the stable steady states are also obtained for various limiting cases of the diffusion rates.

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Authors and Affiliations

  1. Center for Partial Differential Equations, East China Normal University, Minhang, Shanghai, 200241, China

    Xiaoqing He & Wei-Ming Ni

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Wei-Ming Ni

Authors
  1. Xiaoqing He
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  2. Wei-Ming Ni
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Corresponding author

Correspondence to Xiaoqing He.

Additional information

Communicated by P. Rabinowitz.

X. He is supported in part by Postdoctoral Science Foundation of China (No. 2015M580304). W.-M. Ni is supported in part by NSF and NSFC, 111 Project and Recruitment Program of Global Experts in China.

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He, X., Ni, WM. Global dynamics of the Lotka–Volterra competition–diffusion system with equal amount of total resources, II. Calc. Var. 55, 25 (2016). https://doi.org/10.1007/s00526-016-0964-0

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  • DOI: https://doi.org/10.1007/s00526-016-0964-0

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