Wave Speeds for a Time-Periodic Bistable Three-Species Lattice Competition System

Chaohong Pan, Jiali Zhan and Hongyong Wang ()
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Chaohong Pan: School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
Jiali Zhan: School of Mathematics and Physics, University of South China, Hengyang 421001, China
Hongyong Wang: School of Mathematics and Physics, University of South China, Hengyang 421001, China

Mathematics, 2024, vol. 12, issue 20, 1-21

Abstract: In this paper, we consider propagation direction (which can be used to predict which species will occupy the habitat or win the competition eventually) of a bistable wave for a three-species time-periodic lattice competition system with bistable nonlinearity, aiming to address an open problem. As a first step, by transforming the competition system to a cooperative one, we study the asymptotic behavior for the bistable wave profile and then prove the uniqueness of the bistable wave speed. Secondly, we utilize comparison principle and build up two couples of upper and lower solutions to judge the sign of the bistable wave speed which partially provides the answer to the open problem. As an application, we reduce the time-periodic system to a space–time homogeneous system, we obtain the corresponding criteria and carry out numerical simulations to illustrate the availability of our results. Moreover, an interesting phenomenon we have found is that the two weak competitors can wipe out the strong competitor under some circumstances.

Keywords: propagation direction; bistable wave; lattice system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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