Several Types Of Ecosystems, Nonlinear Analysis And Research

Nonlinear analysis of ecological system is an important part of Mathematical ecology. With the development of nonlinear science, the study on it has more and more wide prospects. The nonlinear science which applied can describe,calculate in order to regulate and control the developmental processes and the developmental trend of species, which is one of theoretical basis for people exploiting resources, making use of resources and protecting resources.In the first section, by using the stability theories and the qualitative theories of ordinary differential equation, we study a Kolmogorov system with constant harvesting rate for preys group and analyze the nature of equilibrium points. Then we obtain the sufficient condition of nonexistence and existence to limit cycle under the given parameter satisfied certain conditions, and approved the theoretic analyse by the numerical simulation. At last, the appropriate biological significance of the system is discussed.In the second section, a model of differential equation on nutrient—diatom— N.Scintillans is constructed, based on structural analysis of the essential factors associated with the red tide of N.Scintillans,. Using the methods of the modern nonlinear dynamics, stability and bifurcation behaviors of the model equations are discussed. The value of bifurcation parameter is calculated when Hopf bifurcation was happening and the Mathematical simulation on numerical calculation was also presenented. The results provide scientific basis for predicting and controlling red tide of N.Scintillans to a certain extent.