For A Predator - Prey Population Dynamics Model And Numerical Simulation

Models of population dynamics describe competition and interaction among species or between species and the environment. They can be used to describe, predict and even adjust the growing process and developing trends of species. Models of population dynamics are extensively applied in the management of resources, environmental assessment and management, prevention and control of catastrophes and so on.For the reason that the relationship between predator and prey is one of the basic relationships among species. Recently, the predator-prey models of population dynamics have received a great deal of attention of mathematicians and biologists. Models of population dynamics with the effects of functional response,harvesting control,time delay,stage-structure,age-structure,sex-difference,diffusion have been extensively explored in recent years.The paper contains six chapters. The first chapter is an introduction; The second chapter is concerned with the basic models of population dynamics and the method of model building; Lotka-Volterra predator-prey system,non- Lotka-Volterra predator-prey system and predator-prey systems with harvesting control, time delay, stage-structure ,age-structure ,sex-difference and diffusion are introduced in chapter 3;Chapter 4 and chapter 5 are done by myself. In chapter 4, a mathematical model about two species with stage-structure of predator is deduced. The mathematical model is built based on both the biological characters of coccinella undecimpunctata linnaeus and aphis gossypii and field observations in the cotton fields of Xinjiang of coccinella undecimpunctata preying cotton aphis. Using the tool of difference method, we gain simulated results .The simulated results show that the interaction and change of the two species under different temperature, environmental capacity and initial density. The simulated results are so close to the observational data, so it proved that the model is accurate and useful. On the basis of chapter 4, considering the diffusion of the two species, a predator-prey population dynamical model with age-structure and diffusion effect is deduced, we also gain the time-varying simulated results of the population and distribution of the two species; Chapter 5 gives the future directions of research about the predator-prey models of population dynamics in brief.