Effect of seasonal changing temperature on the growth of phytoplankton

Ming Chen; Meng Fan; Xing Yuan; Huaiping Zhu; Ming Chen; Meng Fan; Xing Yuan; Huaiping Zhu

doi:10.3934/mbe.2017057

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 5&6: 1091-1117. doi: 10.3934/mbe.2017057

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Effect of seasonal changing temperature on the growth of phytoplankton

1.
School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin 130024, China
2.
Department of Mathematics, Dalian Maritime University, 1 Linghai Road, Dalian, Liaoning, 116026, China
3.
School of Urban and Environmental Sciences, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin 130024, China
4.
Lamps and Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada

Received: 01 March 2016 Accepted: 01 October 2016 Published: 01 October 2017
MSC : Primary: 58F15, 58F17; Secondary: 53C35

An non-autonomous nutrient-phytoplankton interacting model incorporating the effect of time-varying temperature is established. The impacts of temperature on metabolism of phytoplankton such as nutrient uptake, death rate, and nutrient releasing from particulate nutrient are investigated. The ecological reproductive index is formulated to present a threshold criteria and to characterize the dynamics of phytoplankton. The positive invariance, dissipativity, and the existence and stability of boundary and positive periodic solution are established. The analyses rely on the comparison principle, the coincidence degree theory and Lyapunov direct method. The effect of seasonal temperature and daily temperature on phytoplankton biomass are simulated numerically. Numerical simulation shows that the phytoplankton biomass is very robust to the variation of water temperature. The dynamics of the model and model predictions agree with the experimental data. Our model and analysis provide a possible explanation of triggering mechanism of phytoplankton blooms.
- Phytoplankton,
- temperature variation,
- ecological reproductive index,
- cyclic dynamics
Citation: Ming Chen, Meng Fan, Xing Yuan, Huaiping Zhu. Effect of seasonal changing temperature on the growth of phytoplankton[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1091-1117. doi: 10.3934/mbe.2017057

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Abstract

An non-autonomous nutrient-phytoplankton interacting model incorporating the effect of time-varying temperature is established. The impacts of temperature on metabolism of phytoplankton such as nutrient uptake, death rate, and nutrient releasing from particulate nutrient are investigated. The ecological reproductive index is formulated to present a threshold criteria and to characterize the dynamics of phytoplankton. The positive invariance, dissipativity, and the existence and stability of boundary and positive periodic solution are established. The analyses rely on the comparison principle, the coincidence degree theory and Lyapunov direct method. The effect of seasonal temperature and daily temperature on phytoplankton biomass are simulated numerically. Numerical simulation shows that the phytoplankton biomass is very robust to the variation of water temperature. The dynamics of the model and model predictions agree with the experimental data. Our model and analysis provide a possible explanation of triggering mechanism of phytoplankton blooms.

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