The diffusive logistic model with a free boundary in heterogeneous environment

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Zhou, Peng¹  Xiao, Dongmei¹ 

[1] Shanghai Jiao Tong Univ, Dept Math, MOE LSC, Shanghai 200240, Peoples R China

关键词: Diffusive logistic model;    Invasive population;    Free boundary;    Heterogeneous environments;    Spreading vanishing;   

DOI  :  10.1016/j.jde.2013.12.008

来源: Elsevier

【 摘 要 】

In this paper, we study the population dynamics of an invasive species in heterogeneous environment which is modeled by a diffusive logistic equation with free boundary condition. To understand the effect of the dispersal rate D and the parameter mu, (the ratio of the expansion speed of the free boundary and the population gradient at the expanding front) on the dynamics of this model, we divide the heterogeneous environment into two cases: strong heterogeneous environment and weak heterogeneous environment. By choosing D and mu, as variable parametors, we deriiie sufficient conditions for species spreading (resp. van-. ishing) in the strong heterogeneous environment; while in the weak heterogeneous environment, we obtain sharp criteria for the spreading and vanishing. Moreover, when spreading happens, we give an estimate for the asymptotic spreading speed of the free boundary. These theoretical results may have important implications for prediction and prevention of biological invasions. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free