Of Lotka-volterra Predation Model Of Analysis And Simulation

Lotka-Volterra model is an important content of population dynamics. This model is extensively applied in ecological balance, protection of plants, creatures and in the control and exploiture of environment. At present, many domestic and foreign scholars have studied this model by theoretical method and applied research. In this paper, Lotka-Volterra models are built and studied under some practical conditions. At first, the solution properties of the models are analyzed. Then, the models are solved by the numerical method. The numerical simulation result conforms to the actual background.This paper includes five chapters. The first chapter called introduction introduce the state of study about biomathematics. The second, third, fourth and fifth chapters are done by myself. In the second part, a predator-prey model of ordinary differential with one-way diffusion is studied considering the monsoon, river flows, other natural conditions and living habits as background. In the third part, a predator-prey model with Monod-Haldane function response and diffusion is built considering that prey play an inhibitory role to predator. Then, stability of the positive equilibrium about this model is analyzed and simulated. In the fourth part, a predator-prey model with Beddington-DeAngelis function response and diffusion is built considering interaction of prey with predator . Then, stability of the positive equilibrium about this model is analyzed and simulated. In the fifth part, the nonautonomous predator-prey system with diffusion and time delays is studied build on before studies and considering environmental periodic change. The periodic solution of this model is analyzed and simulated.