Spatiotemporal Dynamics Of Predator-prey Model Incorporating A Prey Refuge

Spatiotemporal dynamics of predator-prey model plays an important role onthe sustainable use of population natural resources. Among the effects onpredator-prey system, the effects of refuge on the population dynamics are verycomplex. This paper mainly studies the spatiotemporal dynamics ofLeslie-Gower and Ivlev type predator-prey system incorporating refuge. Inchapter1, this paper introduces the background knowledge and the state ofspatiotemporal dynamics behavior of predator-prey system, then describes somerelevant conclusion about effects of refuge on the predator-prey system. Chapter2mainly studies the spatiotemporal dynamics of Leslie-Gower typepredator-prey system incorporating refuge. It gives the stability of equilibriumpoint theory of the model, and the Turing space. Then by the numericalsimulation we show different Turing Patterns. It shows that refuge eventuallyleads to Turing Patterns of the Leslie-the Gower model. In chapter3, withoutdensity restrict, the two types of refuge used by prey on the Ivlev model arestudied by using the analytical approach. Then it investigates with densityrestrict, incorporating refuge, the spatiotemporal dynamics of Ivlev model. Itdiscovers eventually that it may be refuge or density restrict or the result of the role which lead to the generation of patterns. The results will provide thereference for the further study of dynamic spatiotemporal predator-prey system.