On a Conjecture Raised by Yuzo Hosono

  • Ahmad Alhasanat
  • Chunhua OuEmail author


In this paper, we study the speed selection mechanism for traveling wave solutions to a two-species Lotka–Volterra competition model. After transforming the partial differential equations into a cooperative system, the speed selection mechanism (linear vs. nonlinear) is investigated for the new system. Hosono conjectured that there is a critical value \(r_c\) of the birth rate so that the speed selection mechanism changes only at this value. In the absence of diffusion for the second species, we obtain the speed selection mechanism and successfully prove a modified version of the Hosono’s conjecture. Estimation of the critical value is given and some new conditions for linear or nonlinear selection are established.


Lotka–Volterra Traveling waves Speed selection 

Mathematics Subject Classification

35K40 35K57 92D25 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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