Invasion by an inferior or superior competitor: A diffusive competition model with a free boundary in a heterogeneous environment
By Jie Wang, Liangdeng Zhang. 2015
46 citations recorded by the source corpus.
In this study, we consider the population dynamics of an invasive species and a resident species, which are modeled as a diffusive competition process in a radially symmetric setting with a free boundary. We assume that the resident species undergoes diffusion and growth in R-n, while the invasive species initially exists in a finite ball, but invades the environment with a spreading front evolving according to a free boundary. When the invasive species is inferior, we show that if the resident species is already well established initially, then the invader can never invade deep into the underlying habitat, thus it dies out before its invading front reaches a certain finite limiting position. When the invasive species is superior, a spreading-vanishing dichotomy holds, and sharp criteria for spreading and vanishing with d(1), mu, and u(0) as variable factors are obtained, where d(1) mu, and u(0) are the dispersal rate, expansion capacity, and initial number of invaders, respectively. In particular, we obtain some rough estimates of the asymptotic spreading speed when spreading occurs. (C) 2014 Elsevier Inc. All rights reserved.
Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science
View Paper: https://www.semanticscholar.org/paper/9f95de41141ec3b983e342ef52691603d7eac9a4
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In Genetics
In Public Health, Environmental and Occupational Health
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Citations in the corpus
- Existence and uniqueness of solutions of free boundary problems in heterogeneous environments (2019, background): “Recent years, free boundary problems coming from ecology in the spatial heterogeneous environments had been studied by many authors, see [1]-[3], [5]-[7], [9, 10, 12], [14]-[17], for example.”
- Dynamics for a diffusive prey-predator model with different free boundaries (2015, background): “The authors of [10, 15, 32, 33, 47] investigated a competition model in which the invasive species exists initially in a ball and invades into the new environment,”