Single spreading speed and traveling wave solutions of a diffusive pioneer-climax model without cooperative property

Abstract

A diffusive competing pioneer and climax system without cooperative property is investigated. We consider a special case in which the system has no co-existence equilibrium. Under the appropriate assumptions, we show the linear determinacy and the existence of single spreading speed. Furthermore, we obtain the existence of traveling wave solution which connects two boundary equilibria, and also confirm that the spreading speed coincides with the minimal wave speed. The results in this article reveals a phenomenon of strongly biological invasion which implies that the invasion of a new species will leads to the extinction of the resident species.