Dynamics Of A Class Of Competitive-reciprocity Three-species Model With Free Boundary

This dissertation studies the dynamic behavior of a class of competitive–reciprocal three–species model with free boundary,which includes the global existence and unique-ness of the model solution,the uniform boundedness of the solution with respect to time,the comparative principle,and some related properties of invasive species on the free boundary.Firstly,we narrate the relevant background knowledge,and give the corresponding research model.Secondly,in the radial symmetric environment,we use a certain transformation to convert a model with the free boundary into a model with the fixed boundary,and then apply the compression mapping principle and L~ptheory to prove the local existence and uniqueness of the model solution.Next,we obtain the uniform boundedness of the model with respect to time t,and then use the extension method to get the global existence and uniqueness of the model.Besides,we also give the definition of hybrid quasi-monotonic systems,and prove the corresponding comparative principle.Lastly,we study the number of invasive species on the free boundary in the model,the spreading–vanishing dichotomy and large time behavior.In particular,we consider the relationship between the success of invasive species and the width of the free boundary,and the changes of the spread rate for large time after successful dispersal of invasive species.