Speed determinacy of traveling waves for a lattice stream-population model with Allee effect

Chaohong Pan; Xiaowen Xu; Yong Liang; Chaohong Pan; Xiaowen Xu; Yong Liang

doi:10.3934/math.2024913

AIMS Mathematics

2024, Volume 9, Issue 7: 18763-18776. doi: 10.3934/math.2024913

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Research article

Speed determinacy of traveling waves for a lattice stream-population model with Allee effect

Chaohong Pan ¹,
Xiaowen Xu ^{2
,
,},
Yong Liang ^{3
,
,}

1.
School of Mathematics and Statistics, Hunan First Normal University, Changsha, 410205, China
2.
School of Mathematics and Physics, University of South China, Hengyang, 421001, China
3.
School of Mathematics, South China University of Technology, Guangzhou, 510640, China

Received: 13 March 2024 Revised: 23 April 2024 Accepted: 13 May 2024 Published: 04 June 2024
MSC : 35K57, 35B20, 92D25

This paper investigates the speed selection mechanism for traveling wave fronts of a reaction-diffusion-advection lattice stream-population model with the Allee effect. First, the asymptotic behaviors of the traveling wave solutions are given. Then, sufficient conditions for the speed determinacy of the traveling wave are successfully obtained by constructing appropriate upper and lower solutions. We examine the model with the reaction term $ f (\psi) = \psi(1-\psi)(1+\rho\psi) $, with $ \rho $ being a nonnegative constant, as a specific example. We give a novel conjecture that there exists a critical value $ \rho_c > 1 $, such that the minimal wave speed is linearly selected if and only if $ \rho\leq\rho_c $. Finally, our speculation is verified by numerical calculations.
- lattice stream-population model,
- Allee effect,
- traveling waves,
- speed selection
Citation: Chaohong Pan, Xiaowen Xu, Yong Liang. Speed determinacy of traveling waves for a lattice stream-population model with Allee effect[J]. AIMS Mathematics, 2024, 9(7): 18763-18776. doi: 10.3934/math.2024913

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Abstract

This paper investigates the speed selection mechanism for traveling wave fronts of a reaction-diffusion-advection lattice stream-population model with the Allee effect. First, the asymptotic behaviors of the traveling wave solutions are given. Then, sufficient conditions for the speed determinacy of the traveling wave are successfully obtained by constructing appropriate upper and lower solutions. We examine the model with the reaction term $ f (\psi) = \psi(1-\psi)(1+\rho\psi) $, with $ \rho $ being a nonnegative constant, as a specific example. We give a novel conjecture that there exists a critical value $ \rho_c > 1 $, such that the minimal wave speed is linearly selected if and only if $ \rho\leq\rho_c $. Finally, our speculation is verified by numerical calculations.

References

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