A Free Boundary Problem for a Ratio-dependent Predator-prey System
Lingyu Liu
TL;DR
This paper investigates a free boundary problem in a predator-prey system where the boundary is driven by prey dynamics, analyzing long-term behaviors, spreading-vanishing criteria, and asymptotic spreading speed.
Contribution
It introduces a novel free boundary model for a ratio-dependent predator-prey system and establishes criteria for spreading and vanishing, including asymptotic speed analysis.
Findings
Established a spreading-vanishing dichotomy.
Derived criteria for spreading and vanishing.
Provided the asymptotic speed of boundary expansion.
Abstract
In this paper we study a free boundary problem for a ratio-dependent predator-prey system in one space dimension, with the free boundary only caused by the prey. The long time behaviors of solution are discussed. Then we establish a spreading-vanishing dichotomy and the criteria for spreading and vanishing. Finally, when spreading occurs, an accurate limit of the asymptotic speed of h(t) is provided.
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