Qualitive Propertives Of Two Predator-Prey Models

Population ecology is an important branch of ecology science. Since the complexity of ecological relations, mathematical methods and results have been used in and have emerged from ecology. Now population ecology has become the branch that mathematics is most deeply applied in and which is the most systematic one. Early population ecology studies concentrated on local population dynamics. However, it is not enough that populations of organisms are considered only in time. Many ecological processes that are distributed over some spaces should be considered in space. Therefore, ecological models of PDE have attracted considerable attention in recent years.Two predator-prey models are considered in this presentation, two weak- ly Coupled reaction diffusion systems are proposed and qualitives of two systems are given:(a)the stability of non-negative constant steady states, (b)Turing Pattern or Diffusion-driven Instability to the boundary value problem with homogeneous Neumann boundary condition,(c)pattern formation due to the introduction of spatial heterogeneity.This presentation is divided in three parts.In Part 1 the background and history of current research situation about the related work and major work of this presentation are introduced.In Part 2 a predator-prey model with sex structure is studied.The prior estimates for the solutions of the problem are derived.Some sufficient con- ditions for the asymptotic stability around each of the equilibrias are given by using upper and lower solutions method and by constructing a suita-...