Dynamics for a Ratio-Dependent Prey–Predator Model with Different Free Boundaries

Lingyu Liu, Xiaobo Li and Pengcheng Li ()
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Lingyu Liu: School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China
Xiaobo Li: School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China
Pengcheng Li: School of Sciences, Civil Aviation Flight University of China, Guanghan 618300, China

Mathematics, 2024, vol. 12, issue 12, 1-18

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 with each other as time evolves, are used to describe the spreading of prey and predator. Our primary focus lies in analyzing the long-term behaviors of both predator and prey. We establish sufficient conditions for the spreading and vanishing of prey and predator. Furthermore, in cases where spread occurs, we offer estimates for the asymptotic spreading speeds of prey and predator, denoted as u and v , respectively, as well as the asymptotic speeds of the free boundaries, denoted by h and g . Our findings reveal that when the predator’s speed is lower than that of the prey, it leads to a reduction in the prey’s asymptotic speed.

Keywords: free boundary; ratio-dependent model; spreading and vanishing; long-term behaviors; asymptotic speed (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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