Stability property of the prey free equilibrium point

We revisit a prey-predator model with stage structure for predator, which was proposed by Tapan Kumar Kar. By using the differential inequality theory and the comparison theorem of the differential equation, we show that the prey free equilibrium is globally asymptotically stable under some suitable...

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Bibliographic Details
Main Author: Yue Qin
Format: Article
Language:English
Published: De Gruyter 2019-07-01
Series:Open Mathematics
Subjects:
Online Access:https://doi.org/10.1515/math-2019-0051
Description
Summary:We revisit a prey-predator model with stage structure for predator, which was proposed by Tapan Kumar Kar. By using the differential inequality theory and the comparison theorem of the differential equation, we show that the prey free equilibrium is globally asymptotically stable under some suitable assumption. Our study shows that although the predator species has other food resource, if the amount of the predator species is too large, it could also do irreversible harm to the prey species, and this could finally lead to the extinction of the prey species. Our result supplement and complement some known results.
ISSN:2391-5455