On a Conjecture Raised by Yuzo Hosono

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 syst...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2019-03, Vol.31 (1), p.287-304
Main Authors: Alhasanat, Ahmad, Ou, Chunhua
Format: Article
Language:English
Subjects:
Applications of Mathematics
Diffusion rate
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Traveling waves
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Summary: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.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-018-9651-5