Nonlinear Dynamic And Statistical Mechanical Features Of Lake Eutrophication

Lake eutrophication is a classical academic and industrial difficult issue. Lake eutrophication forms a very complex ecological community as an open, nonlinear system far from equilibrium in which a variety of complex physical, chemical and biological reactions occur. The traditional linear research technique and model could not yet reveal its intricate mechanism. From a new perspective, in the present paper, the nonlinear method is applied to gradually investigate formation mechanism of lake eutrophication and its spatial-temporal pollution distribution.For the temporal dynamics, the paper proposes a one-dimensional single-box phosphorus cycling model for the interactions among particulate phosphorus, dissolved reactive phosphorus and P in the alga. Assuming the lake is P-limited, nonlinear dynamic analyses on the model are then invoked to reveal that coexisting of three forms of phosphorus will dominate the dynamic trends of the system. Dynamic evolutions of three types of phosphorus concentrations are numerically elaborated. Furthermore, for the sake of practical interests, considering that the concentrations of three types of phosphorus may be largely affected by the sediments, numerical simulations are carried out with the inclusions of the sediments effects, which is expressed as the fluctuation of the disturbing conditions in the model. The present research may not only theoretically highlight the dynamic mechanisms of phosphorus cycle but also shed new lights on industrial applications such as eutrophication prevention.On the spatial structure research, a novel mathematical model basing on statistical mechanics and maximum flux principle is established, which pays more attention to the spatial structure of system than available methods and is of more profound significance. By invoking Self-Organization Feature Map (SOM), the novel model can elucidate the characters of eutrophication more clearly. The new model is further applied on ten typical lakes and the results show that the method is reasonable and practicable. Last but not least, it is pointed out that the novel model is also promising for the predictions of lake water eutrophication.Furthermore, considering Multi-scale analysis, a new model is established from microscopic dynamic viewpoints and simulations are conducted by invoking Self-Organization Feature Map (SOM). Basing on the non-equilibrium statistical mechanics, the article discusses the non-linear interactions of nutrients and its diffusion from microscopic dynamic viewpoints. Spatial fractal structure of the nutrients through self-organization and its effects on lake eutrophication are analyzed. A novel framework for lake eutrophication is thus systematically constructed. By invoking Self-Organization Feature Map (SOM), the new model is further applied on Tai Lake partial basins and Dian Chi Lake. The results show that the lake system nutrients distribution is almost fractal, and more detailed studies reveal the distribution has multi-fractal characteristics changing with spatial scales. This suggests the lake system has the diverse distributed structures of nutrients and thus changeable eutrophication along the basin. Grasping the lake system nutrients diffusion dynamic mechanism and its spatial fractal structures is doubtlessly of vital significance to the monitors, controls and predictions of lake eutrophication.