Math. Model. Nat. Phenom.
Volume 15, 2020
|Number of page(s)||26|
|Published online||03 December 2020|
Dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries*
School of Mathematics and Big Data, Foshan University,
528000, PR China.
2 Shenzhen JL Computational Science and Applied Research Institute, Shenzhen 570100, PR China.
3 School of Mathematics and Statistics, Central South University, Changsha 410083, PR China.
** Corresponding author: firstname.lastname@example.org
Accepted: 29 July 2020
This paper focuses on the dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries in one dimensional space, in which the free boundaries represent expanding fronts of top predator species. The existence, uniqueness and estimates of the global solution are discussed firstly. Then we prove a spreading–vanishing dichotomy, specifically, the top predator species either successfully spreads to the entire space as time t goes to infinity and survives in the new environment, or fails to establish and dies out in the long run. The long time behavior of the three species and criteria for spreading and vanishing are also obtained. Besides, our simulations illustrate the impacts of initial occupying area and expanding capability on the dynamics of top predator for free boundaries.
Mathematics Subject Classification: 35K51 / 35R35 / 92B05 / 35B40
Key words: Ratio-dependent food chain model / double free boundaries / spreading–vanishing dichotomy / long time behavior
© The authors. Published by EDP Sciences, 2020
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