Dynamics for a Ratio-dependent Prey-predator Model with Different Free Boundaries

TL;DR

This paper analyzes a ratio-dependent prey-predator model with two free boundaries representing spreading fronts, providing conditions for spreading or vanishing and estimating long-term speeds of prey and predator expansion.

Contribution

It introduces a novel prey-predator model with separate free boundaries and derives conditions and estimates for their long-term behaviors.

Findings

Conditions for prey and predator spreading or vanishing.

Asymptotic spreading speeds of prey and predator.

Behavior of free boundaries over time.

Abstract

In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time evolves, are used to describe the spreading of prey and predator. We mainly investigate the longtime behaviors of predator and prey. Then some sufficient conditions for spreading and vanishing are given. In addition, when spreading occurs, some estimates of asymptotic spreading speeds of u, v and asymptotic speeds of h, g are provided.