GLOBAL DYNAMICS OF TWO PHYTOPLANKTON-ZOOPLANKTON MODELS WITH TOXIC SUBSTANCES EFFECT

Shanshan Chen; Hong Yang; Junjie Wei

doi:10.11948/2156-907X.20180187

2019 Volume 9 Issue 2

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Shanshan Chen, Hong Yang, Junjie Wei. GLOBAL DYNAMICS OF TWO PHYTOPLANKTON-ZOOPLANKTON MODELS WITH TOXIC SUBSTANCES EFFECT[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 796-809. doi: 10.11948/2156-907X.20180187

Citation:

Shanshan Chen, Hong Yang, Junjie Wei. GLOBAL DYNAMICS OF TWO PHYTOPLANKTON-ZOOPLANKTON MODELS WITH TOXIC SUBSTANCES EFFECT[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 796-809. doi: 10.11948/2156-907X.20180187

GLOBAL DYNAMICS OF TWO PHYTOPLANKTON-ZOOPLANKTON MODELS WITH TOXIC SUBSTANCES EFFECT

1.
Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, 264209, China
2.
School of Mathematics and Big Data, Foshan University, Foshan, Guangdong, 528000, China

Corresponding author: Email address:weijj@hit.edu.cn(J. Wei)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 11771109)

Abstract

Abstract

In this paper, we investigate phytoplankton-zooplankton models with toxic substances effect and two different kinds of predator functional responses. For Holling type Ⅱ predator functional response, it is shown that the local stability of the positive equilibrium implies global stability if there exists a unique positive equilibrium. When there exist multiple positive equilibria, the local stability of the positive equilibrium with small phytoplankton population density implies that the model occurs bistable phenomenon. These results also hold for Holling type Ⅲ predator functional response under certain conditions.
- Phytoplankton-zooplankton /
- global stability /
- bistable phenome-non
MSC: 34D20

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References

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