A diffusive Lotka–Volterra model with Robin boundary condition and sign-changing growth rates in time-periodic environment. (August 2023)

• Record Type: Journal Article
• Authors: Zhang, Shunqin; Zhu, Xuege; Liu, Xiaowei
• Is Part Of: Nonlinear analysis. Volume 72(2023)
• Publication Date: 2023-08
• Subjects: Lotka–Volterra model -- Robin boundary condition -- Spreading–vanishing dichotomy -- Sign-changing growth rates -- Heterogeneous time-periodic environment; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2023.103856
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, a Lotka–Volterra model with Robin and free boundary conditions is considered in the heterogeneous time-periodic environment. We mainly consider the changes of local growth rates of native and invasive species that might be negative in some large regions. We study the spreading–vanishing dichotomy. When vanishing occurs, a native species cannot spread successfully as time goes to infinity. However, for an invasive species, in the long run, either it will go extinct or converge to the unique positive solution of time-periodic boundary value problem of logistic equation. When spreading occurs, both native and invasive species have upper and lower bounds. We also obtain the criteria for spreading and vanishing, and estimate of the asymptotic spreading speed.