Spatial Pattern Dynamics Of Several Predator-prey Models

In population dynamics,the predator-prey model has become a classical model due to its large and rich dynamic characteristics.When there are native species in the habitat,we investigate the interspecies relationship with species invasion.The spreading speed of invasive species is an important topic.This article studies three types of three-species predator-prey models and obtains the spreading speed of invasive species in different models.Then the main content of this article is explained:In the second chapter,a three-species predator-prey with a period of time is studied.In this model,the two prey species are in a competitive relationship.The predator and one of the prey species invade as alien species.Under certain assumptions,we described the long-term behavior of invasive species and estimated the spreading speed of invasive species.In the end,we got the conclusion that the existence of predator-related species will affect each other's invasion speed.In Chapter 3,we examine a three-species predator-prey model with nonlocal diffusive.In this model,two prey species with low interspecies competition are used as native species and the predator is invaded as an alien species.The first step,we put out the existence and the overall stability of the positive equilibrium point of the model.The second step,we consists in determining the speed of asymptotic propagation of invasive species through the theory of semigroups.The third step,we give some specific examples and obtain the spreading speed of invasive species in the model.In Chapter 4,a three-species predator-prey model with time delays and non-linear predation rates is investigated.We focus on the effects of time delay and nonlocal effects on the spreading speed of species invasion.