Traveling Wave Solutions In A Phytoplankton-Zooplankton Reaction-Diffusion Model With Delay And Advection

In this paper we mainly study the traveling wave solutions in a phytoplankton-zooplankton reaction-di?usion model with delay and advection. Consider that some phytoplankton can liberate toxin which harms to the zooplankton and some zooplankton can be harvested for food. From reality, we also consider the time delay which assumes that a duration of τ time units elapses when an individual phytoplankton is consumed and the moment when the corresponding addition or reduction(due to toxin)is made to the zooplankton population. We also consider the cases that species live in the media where the di?usion moves to a certain direction which caused by water to make the model more realistic. There are three chapters in our paper, the first chapter is the introduction of the background of our problem and our mathematics model. Then the second chapter are some preliminaries of our problem including equilibria and stability and abstract result for delayed recursion. At last, the third chapter is the whole proof of our main theorem 3.1. We will show that there exists a finite positive number c*that can be characterized as the slowest spreading speed of traveling wave solutions connecting a mono-culture with the coexistence equilibrium by using our abstract result for general delayed recursion model established in [17].