The Dynamics Of A Leslie-Gower Nonlocal Dispersal Predator Model With Free Boundaries

As we know,evolution,diffusion,and propagation of a certain species are important issues in the spatial ecology.Additionally,the interaction among several species,such as cooperation,competition,and predator-prey,etc.,is also an important topic in this areaWhen an exotic species locally invades a habitat in which another species already inhabits,the size of the habitat of the invasive species changes as time goes by.Meanwhile,the number of these two species also changes with the changes of time.We assume that the interaction between the invasive species and the native species is predator-prey Furthermore,we assume that these two species can move between non-adjacent locations To analyze these kinds of ecological problems precisely and quantitatively,we research a Leslie-Gower nonlocal dispersal predator model with free boundaries in this dissertation This model simulates the evolution,diffusion and propagation of both an invasive species in a one-dimensional local habitat with free boundaries and a native species in the one-dimensional whole space.In particular,the free boundaries in the model represent the spread front of this given one-dimensional habitat in which the invasive species inhabitsIn the first chapter of this dissertation,by reviewing many applications of both reaction-diffusion equations and nonlinear free-boundary models in the spatial ecology.we introduce the model being researched in this dissertation.We also summarize main methods and results of this dissertation in this chapter.In the second chapter,we prove the existence and uniqueness of the solutions of this model when time t ?(0,+?).In the next chapter,we analyze and examine its long-time dynamical behaviors.To be precise.we obtain a spreading-vanishing dichotomy for the invasive species and some sharp criteria for spreading and vanishing.In the final chapter,some discussion and research prospect are done briefly.Another thing worth noting is that the term v/u which appears in the predator equation of the model might not satisfy the local Lipschitz condition regarding u when u nears zero,which causes some difficulties to our study.Finally,We successfully deal with the aforementioned difficulties via proving some positive lower bounds of u which is the solution of the model.