The Study On Spatio-temporalevolution And Integrated Management Strategies Of Phytoplankton

On the problems of eutrophication, algal bloom and red tide, etc.,which caused ecological disasters and leaded to economic problems andhuman health problems, exploring the effective way to control planktonbloom and red tide is very urgent. Based on this, according to biology,ecology and mathematical theory, the present paper discusses somedynamical problem concerning plankton, and investigates the integratedmanagement strategies of plankton. Then the corresponding managementstrategies can be obtained.Firstly, the spatio-temporal evolution of plankton is studied. Bymathematical theories and biological significance, a nutrient-planktonmodel is proposed, which is addressed by a couple of reaction-advection-diffusion equations. Focused on studies on the influence of nutrient inputand phytoplankton sinking on the system, the results show that the effectof nutrient input and phytoplankton sinking on changes of phytoplanktonconcentration is great. In particular, the relationship between nutrientinput and the increase of phytoplankton concentration is positivecorrelation. The numerical results confirm the theoretical results further.Secondly, the integrated management strategies of plankton areinvestigated, a phytoplankton-fish (or plankton) integrated managementmodel is given. The artificial control and biological control carry out atthe same time in the model. The control is called artificial control, but thebiological control. Results show that the concentration of phytoplanktoncan be always contained at some a level by the artificial control, but theprice paid is much more, and the frequency of control carried out is muchhigher. When the biological control is considered, the frequencydecreases, and the price paid is relatively small. Not only is the concentration of phytoplankton controlled at some a level, but also thecorresponding economic value can be brought about.Finally, the asynchronous control of plankton is studied. Establishedearly warning value before phytoplankton bloom is the characteristic ofthis kind of control. When the concentration of phytoplankton reaches thewarning value, the biological control will occur. While the concentrationof phytoplankton reaches the critical value of phytoplankton bloom, theartificial control or both artificial control and biological control will becarried out. Using geometric method, the existence and stability ofperiodic solution in the system is discussed. By numerical technology, theaccuracy of theory obtained is inspected. The discussion on the systemwill base on all of these results. At last, the advantage and disadvantagebetween synchronous control and asynchronous control are discussed byusing numerical techniques.