The sign of bistable wave speed for a plankton model

Abstract

The sign of the speed of bistable traveling wave solution is an important focus in the field of population dynamics, since it can be used to predict which species will win the competition and ultimately survive. In this paper, the sign of bistable wave speed of a plankton model with cubic nonlinearity is studied. By a delicate analysis, a sufficient condition for bistable wave to be stationary is first obtained. Symmetric and multiplication properties for stationary bistable wave are established. By upper-lower solution method and comparison principle, two sufficient conditions are found so that the bistable wave speed is negative or positive. Moreover, numerical simulations are performed to illustrate our theoretic conclusions.