Abstract
The aim of this paper is to investigate the dynamics of the solution for a class of reaction-diffusion-advection logistic model with a free boundary in heterogeneous environment. The species undergoes diffusion and advection in a one dimensional heterogeneous environment, and it invades the environment with a spreading front evolving as the free boundary. To understand the effects of the advection rate α and the expansion capacity μ on the dynamics of this model, we derive a spreading-vanishing dichotomy and obtain the sharp criterion for the spreading and vanishing by choosing α and μ as variable parameters. That is, the invasion species can unconditionally survive for a slow advection rate, while, for a fast advection rate, whether it can survive or not depends on the expansion capacity and initial values of the invasion species.
Highlights
Due to the serious threat of invasive species to bio-diversity conservation and the global economy, mathematical modeling has become an important tool in analyzing the prediction and prevention of biological invasions [, ]
The aim of this paper is to study the effects of advection and the free boundary condition on the dynamics of model ( . ) in the heterogeneous environment
6 Discussion In this paper, we incorporated the free boundary and heterogenous environment into the reaction-diffusion-advection logistic model, which is more realistic for describing the invasion dynamics of a new species, investigated the influence of the advection term and spatial heterogeneous environment features on the dynamics of the invading species, and gave a rough estimates of the asymptotic spreading speed
Summary
Due to the serious threat of invasive species to bio-diversity conservation and the global economy, mathematical modeling has become an important tool in analyzing the prediction and prevention of biological invasions [ , ]. A great deal of attention has been paid to developing more realistic mathematical models for the invasion dynamics. There have been a number of works on modeling the invasion of a species described by a reaction-diffusion system; see [ – ] and the references cited therein for further details. There is growing interest in modeling and understanding spatial species dynamics in advection environments, i.e., environments where individuals are exposed to unidirectional flow or biased dispersal [ ]. Water flow imposes directional bias (advection) buoyancy and turbulence leads to unbiased movement (diffusion) [ ].
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