Stability Analysis Of Predator-prey Models With Diffusion

If the living environment for species is destroyed or changed, it can be saved by through of natural adjustment between species and migration of its living environment, that is, diffusion in various patch systems, to keep species'permanent living Researches in this respect can be used to forecast and control species'change and development trend. Based on predator-prey model with diffusion, this paper makes a research on sufficient conditions for species'bound, persistence and stability in the ecological system.First, a ratio-dependent predator-prey model with diffusion is studied. The existence of the positive equilibrium point is obtained by algebraic equation and analysis of functional graph. Sufficient conditions for the bound and persistence of the solution are established by using the comparison principle theorem. Global stability of the positive equilibrium is discussed by constructing a suitable Liapunov function.Second, taking the impacts caused by delay factors into species, a Lotka-Volterra predator-prey model with diffusion, discrete and continuous delay is considered. The existence of the positive equilibrium point is obtained by algebraic equation and analysis of functional graph. The persistence and bound of the solution are obtained by using differential inequality. The global stability in the positive equilibrium point is obtained by using a Liapunov functional method.Last, taking in mind practical impacts caused by coefficients in the model of being variables, the conclusions will be extended to a diffusive model with time delay and Holling typeШfunctional response. The persistence and bound of the solution are obtained by using differential inequality. The method and structure of the Liapunov functional are attempted from different perspective. Global stability of the solution is discussed by constructing a suitable Liapunov functional.