Types Of Differential Equation Model Of Qualitative Analysis

In this paper, by using the stability theories and the qualitative theories of ordinary differential equations, several differential equation models under the Autonomous and Nonautonomous were studied, qualitative behavior of trajectories was obtained;In chapter two, a qualitative behavior of prey-predator system with sparssing effect was study. The topological structure of the trajectories of this system in first quadrant was analysed. At the same time, some biological illustrations were also given. The globally asymptotical stability of the positive equilibrium point of this system was proved if it was stable under some certain conditions, so, this system had not limit cycles at all;In chapter three, the qualitative behavior of the solution of a nonlinear differential dynamical system on bio-chemical reaction was studied. The necessary and sufficient condition of the existence and uniqueness of the limit cycles in this system was completely solved, and then the variance of limit cycle as the changing of parameter was discussed. In chapter four, the mixed model with predatoriness and competition of three species was discussed, in which predator had Holling functional response. It was proved that the system had exactly one positive globally asymptotical stability periodic solution and almost periodic solution.