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A mathematical model of algal blooms based on the characteristics of complex networks theory

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  • Yao, Jianyu
  • Xiao, Peng
  • Zhang, Yunhuai
  • Zhan, Min
  • Cheng, Jiangwei

Abstract

To predict the outbreak time of algal blooms and its duration in an actual body of water, this paper developed a directed complex networks (CNs) model of algal blooms. This new model was based on the characteristics of CNs theory and the primary factors that influenced algal blooms. By calculating the shortest path and proposing a key degree node model, the role of each influencing factor during algal blooms was evaluated. Based on years of on-site monitoring data (collected from 1992 to 2000) concerning the Han River, a statistical characteristic function G that reflected the relationship between the statistical characteristics of dominant algae blooming and the degree of algal blooms pollution was proposed. The results indicate that the proposed function G is capable of effectively and semi-quantitatively characterizing the outbreak time and the duration of algal blooms. If the value of G in a body of water is less than 32.6, the body of water will outbreak an algal bloom. An increasingly smaller of G value indicates a greater degree of algal blooms pollution and longer bloom duration.

Suggested Citation

  • Yao, Jianyu & Xiao, Peng & Zhang, Yunhuai & Zhan, Min & Cheng, Jiangwei, 2011. "A mathematical model of algal blooms based on the characteristics of complex networks theory," Ecological Modelling, Elsevier, vol. 222(20), pages 3727-3733.
    • Handle: RePEc:eee:ecomod:v:222:y:2011:i:20:p:3727-3733
    DOI: 10.1016/j.ecolmodel.2011.09.006
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    References listed on IDEAS

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    1. Long, Tian-yu & Wu, Lei & Meng, Guo-hu & Guo, Wei-hua, 2011. "Numerical simulation for impacts of hydrodynamic conditions on algae growth in Chongqing Section of Jialing River, China," Ecological Modelling, Elsevier, vol. 222(1), pages 112-119.
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    4. Galvão, Viviane & Miranda, José G.V., 2008. "A computational model for cancer growth by using complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5279-5286.
    5. Elgazzar, A.S., 2003. "Applications of small-world networks to some socio-economic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 402-407.
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    1. Zhao, Xiaodong & Zhang, Hongjian & Tao, Xiaolei, 2013. "Predicting the short-time-scale variability of chlorophyll a in the Elbe River using a Lagrangian-based multi-criterion analog model," Ecological Modelling, Elsevier, vol. 250(C), pages 279-286.
    2. Du, Xiangjun & Shao, Fengjing & Wu, Shunyao & Sun, Rencheng & Wang, Changying, 2017. "Complex network modeling for mechanisms of red tide occurrence: A case study in Bohai Sea and North Yellow Sea of China," Ecological Modelling, Elsevier, vol. 361(C), pages 41-48.

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