A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model

Abstract

In this paper we study a ratio-dependent predator-prey model with a free boundary caused by predator-prey interaction over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing dichotomy; namely, as t goes to infinity, both prey and predator successfully spread to the whole space and survive in the new environment, or they spread within a bounded area and eventually die out. The criteria governing spreading and vanishing are obtained. Finally, when spreading occurs we provide some estimates to the asymptotic spreading speed of the moving boundary h(t).

Keywords

• free boundary
• ratio-dependent model
• spreading-vanishing dichotomy
• criteria
• asymptotic speed