Dynamics of a periodic stoichiometric model with application in predicting and controlling algal bloom in Bohai Sea off China

Da Song; Meng Fan; Ming Chen; Hao Wang; Da Song; Meng Fan; Ming Chen; Hao Wang

doi:10.3934/mbe.2019006

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 119-138. doi: 10.3934/mbe.2019006

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Dynamics of a periodic stoichiometric model with application in predicting and controlling algal bloom in Bohai Sea off China

1.
School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R. China
2.
School of Science, Dalian Maritime University, 1 Linghai Road, Dalian, Liaoning, 116026, P. R. China
3.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

Received: 09 September 2018 Accepted: 14 September 2018 Published: 11 December 2018

We develop a nonautonomous stoichiometric algal growth model incorporating a seasondriven light intensity. We characterize the model dynamics by showing positive invariance, dissipativity, boundary dynamics, and internal dynamics. We use numerical simulations to uncover the impacts of the seasonal light intensity and the nutrient availability on the algal dynamics. We discuss two control methods, removing algae (RA) periodically and blocking nutrient (BN) input from rivers constantly, via our modeling approach. By comparison, the BN method is a more effective way to terminate algal bloom in Yellow Sea off China. The model dynamics can fit the Bohai Sea data well. Our model and analysis provide a possible explanation of seasonal algal bloom and give some measurements for controlling algal bloom in China's coastal regions.
- stoichiometric model,
- algal bloom,
- seasonal light,
- nutrient,
- control method,
- Bohai Sea,
- qualitative analysis
Citation: Da Song, Meng Fan, Ming Chen, Hao Wang. Dynamics of a periodic stoichiometric model with application in predicting and controlling algal bloom in Bohai Sea off China[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 119-138. doi: 10.3934/mbe.2019006

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Abstract

We develop a nonautonomous stoichiometric algal growth model incorporating a seasondriven light intensity. We characterize the model dynamics by showing positive invariance, dissipativity, boundary dynamics, and internal dynamics. We use numerical simulations to uncover the impacts of the seasonal light intensity and the nutrient availability on the algal dynamics. We discuss two control methods, removing algae (RA) periodically and blocking nutrient (BN) input from rivers constantly, via our modeling approach. By comparison, the BN method is a more effective way to terminate algal bloom in Yellow Sea off China. The model dynamics can fit the Bohai Sea data well. Our model and analysis provide a possible explanation of seasonal algal bloom and give some measurements for controlling algal bloom in China's coastal regions.

References

[1]	G. Ahlgren, Temperature functions in biology and their application to algal growth constants,. Oikos, 49 (1987), 177–190.
[2]	J.H. Landsberg, The effects of harmful algal blooms on aquatic organisms, Rev. Fisher. Sci., 10 (2002), 113–390.
[3]	X. Li and H.Wang, A stoichiometrically derived algal growth model and its global analysis, Math. Biosci. Eng., 7 (2010), 825–836.
[4]	Y. Qi, Z. Zhang, Y. Hong, S. Lu, C. Zhu, and Y. Li, Occurrence of red tides on the coasts of China, In T.J. Smayda, and Y. Shimizu (Eds.) Toxic Marine Phytoplankton, Elsevier, Amsterdam, (1993), 43–46.
[5]	S. Tan, G. Shi, J. Shi, H. Gao, and X. Yao, Correlation of Asian dust with chlorophyll and primary productivity in the coastal seas of China during the period from 1998 to 2008, J. Geophys. Res., 116 (2011), doi:10.1029/2010JG001456.
[6]	C.K. Tseng, M.J. Zhou, and J.Z. Zou, Toxic phytoplankton studies in China, In T. J. Smayda, and Y. Shimizu (Eds.) Toxic Marine Phytoplankton. Elsevier, Amsterdam, (1993), 347–452.
[7]	T. Yan, M.J. Zhou, and J.Z. Zou, A national report on harmful algal blooms in China, In: Taylor “Max”, F. J. R. & V. L. Trainer (eds.). Harmful algal blooms in the PICES region of the North Pacific. PICES Scientific Report No. 23. North Pacific Marine Science Organization, Sidney, BC, Canada, (2002), 119–128.
[8]	R.E. Gaines and J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977.

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