Study Of Mathematical Model Of Algal Blooms Based On Complex Networks Theory

The number and scale of eutrophic waterbody in our country have rank first in the world. The eutrophication in water has become one of the most important social and environmental problem that seriously threat water security and resources. The construction of the Three Gorges Reservoir bring great economic benefits to human, and increase the pressure of eutrophication in the reservoir regions. Using the method and theory to study the eutrophication of water from the angle of mathematics, it plays an important role in the ecological significance and the theoretical guiding meaning.The characteristics of complex networks (CNs) takes on universal characteristic, is a nonlinear phenomenon that is widely appeared in nature. The phenomenon agrees with the behavior of amount of algae aggregation when algal blooms. The substance of algal blooms is a statistical result of assembling in a short time in partial region of large area. Therefore, it is feasible to build and analyze the overall simulation model and the theoretical framework of algal blooms by the characteristics of CNs.Based on the synchronization of CNs and kinetic mechanism of algal growth, and according to numbers of references and years of on-site monitoring data, this paper studies the primary factors that influenced algal blooms. From the description of shortest path between each influencing factor during algal blooms, we developed a directed complex networks (CNs) model of algal blooms according to the characteristics of CNs theory (the average path length, clustering coefficient, the degree of node, and betweenness). At the same time, the paper evaluated the role of each influencing factor during algal blooms. 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 water environmental quality was proposed. In the paper, the statistical properties of algae during the algal blooms is verified from the perspective of CNs characteristics, which reveals that the phenomenon of algal blooms is a statistical result of multi-factor interaction and multi-dimensional cooperation in water body during algal blooms. The results indicate that the statistical characteristic function G can effectively represent the outbreak time, degree of pollution, duration and scale during algal blooms in a semi-quantitative way.The paper also uses the method of clustering analysis to classify the continuous monitoring data of Feb. and Mar. in the Han River from 1992 to 2000, the results show that this method can be used to predict the possibility of outbreaking algal blooms in the same water body in the future, but does not apply in the classification analysis of two or more water bodies.