Geodesic
Dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries
Dawei Zhang1 ; Beiping Duan2 ; Binxiang Dai3
1 School of Mathematics and Big Data, Foshan University, Foshan 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.
Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 62.

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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.
DOI : 10.1051/mmnp/2020034

Dawei Zhang 1 ; Beiping Duan 2 ; Binxiang Dai 3

1 School of Mathematics and Big Data, Foshan University, Foshan 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. 
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Dawei Zhang; Beiping Duan; Binxiang Dai. Dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries. Mathematical modelling of natural phenomena, Tome 15 (2020), article  no. 62. doi : 10.1051/mmnp/2020034. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2020034/

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