Dynamic Analysis Of Density Evolution Of Red Tide Algae

Red tide is a kind of abnormal phenomenon in the marine ecosystem. It is caused by red tide algae in the family of an explosive proliferation with specific conditions, that results the serious pollution of ocean. The reason of the red tide occurred is that the industrial waste water and domestic sewage discharged into the ocean with large amounts of inorganic nutrients and organic matter causes the eutrophication of the sea water. The nutrients is the material basis for the formation of red tide.Chaetoceros compressus belongs to the temperate coastal species, and it is easy to find in low temperature season and distributed in China coast. Importing into the model of large ecosystem dynamics, based on analyzing the modeling of ecological system, and related to the elimination of the nutrient change and process of growth and death of algae as the core modeling the establishment of the global ecological system. We consider the external environment variable of the system to study the change of state variables in the system.In this paper we investigate the interrelation between the concentration of nu-trients and the density of Chaetoceros and algae I (algae with appropriate external replenishment), we establish mathematic model to describe the dynamic evolution behaviors between the three; The stability state of material evolutionary process in the model is analyzed and judged by Routh-Hurwitz criterion; And we select the increase rate of the concentration of nutrients as the key parameter. We could get the conditions when Hopf bifurcation occurs in the system. At the end, through numerical simulation, we calculate Lyapunov Exponent spectrum and parameter threshold when Hopf bifurcation occurs in the system. The result indicates that the concentration of nutrients play a vital role in the change of system state. And then this helps to identify the evolutionary mechanism of the system to produce the bifurcation and chaos phenomena. Finally we get the method to restrain the blooms of red tide through controlling the key parameter.We investigate the interrelation between the concentration of nutrients and the density of algae and zoo-plankton, we establish mathematical model to describe the dynamic evolution behaviors between the three; The stability state of material evolutionary process in the model is analyzed and judged by Routh-Hurwitz cri-terion; Through numerical simulation, we calculate Lyapunov Exponent spectrum and parameter threshold when Hopf bifurcation occurs in the system. We consider the condition that the rate of growth and death of algae and zoo-plankton disturb respectively by the Gaussian white noise, we establish stochastic mathematical model to the three.We found that in the case of random disturbance the system generate small bounded chaos phenomenon through the numerical simulation of the stochastic system.In each section, simulations are carried out to conform to our conclusions.