Analysis Of Chemotaxis Model For Multi-species Host-parasitoid Interactions

This paper deals with a mathematical model of multi-species host-parasitoid interactions. The way how the host-parasitoid system comes into being and the complicated chemotaxis between organisms are introduced.The background of the paper and the origin of the subject is given.And the model is analyzed and studied by mathematical theory.Two parasitoids aggregate in response to volatile infochemicals emitted by the crops that the two hosts are feeding upon,then kill the pests hosts.The model consists of five reaction-diffusion-chemotaxis equations.By a fixed point method,we prove local existence and uniqueness.Together with Schauder theory, L~p estimates and up-down solution method of parabolic equations we prove the existence and uniqueness of a global solution.Furthermore,the non-existence of non-constant steady state is studied.Simplify the system by setting M=0,Q=0.The chemotaxis-driven instability for a sub-model is also analytically proved by perturbation analysis when the coefficientχP is large.