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Mutual inclusion in a nonlocal competitive Lotka Volterra system

  • Xiaojie HouEmail author
  • Biao Wang
  • Zhengce Zhang
Original Paper Area 1

Abstract

We investigate the traveling front solutions of a nonlocal Lotka Volterra system to illustrate the outcome of the competition between two species. The existence of the front solution is obtained through a new monotone iteration scheme, the uniqueness of the front solution corresponding to each propagation speed is proved by sliding domain method adapted to nonlocal systems, and the asymptotic decay rate of the fronts with critical and noncritical wave speeds is derived by a new method, which is different from the single equation case. The results demonstrate that in the long run, two weakly competing species can co-exist.

Keywords

Nonlocal Lotka Volterra Traveling front Asymptotic behavior Uniqueness 

Mathematics Subject Classification (2000)

Primary 35B35 Secondary 91B18 35K57 35B40 

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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of North Carolina WilmingtonNCUSA
  2. 2.School of Mathematics and Statistics, Xi’an Jiaotong UniversityXi’anChina

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