Propagation dynamics of a Lotka–Volterra competition model with stage structure in time–space periodic environment. (October 2022)

• Record Type: Journal Article
• Authors: Zhao, Xiao; Yuan, Rong
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Lotka–Volterra competition model -- Stage structure -- Time–space periodic -- Principal eigenvalue -- Pulsating wave; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103575
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a diffusive Lotka–Volterra competition model with stage structure and time–space periodic habitats. Firstly, we investigate that the system has two periodic semi-trivial solutions ( u ∗ ( t, x ), 0 ) and ( 0, v ∗ ( t, x ) ) . Next, the existence of the principal eigenvalue for the eigenvalue problem associated with a linear time–space periodic reaction–diffusion cooperative system with time delay is established. By using eigenvalue functions and semi-trivial solutions, we construct upper and lower solutions. Then by Schauder's fixed point, there is a pulsating wave solution ( U ( t, x, x + c t ), V ( t, x, x + c t ) ) connecting ( 0, v ∗ ( t, x ) ) and ( u ∗ ( t, x ), 0 ) .