In the study of reaction-diffusion equation,it is very effective to construct stationary solutions and traveling wave solutions by using the phase plane analysis.In this paper,we firstly use this method to concisely analyze the phase plane of the combustion equation,and obtain the existence of stationary solutions and traveling wave solutions,then we discuss the monostable equation,bistable equation and other types of equations.Based on this,we study the dynamic behavior of the spreading of specie in a river ecosystem model.For the problem that many equations have common junctions,we use the phase diagram of a single equation by the superposition of variable scale,give detailed phase diagram analysis of related problems and obtain the existence of stationary solutions.Finally,we extend the problem to more general and complicated cases,such as four branching rivers,we can also obtain the existence of stationary solutions. |