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A new study for the global asymptotic stability of a general predator-prey model
  • Manh Tuan Hoang
Manh Tuan Hoang
FPT University
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Abstract

In a previous paper [L. M. Ladino, E. I. Sabogal, Jose C. Valverde, General functional response and recruitment in a predator-prey system with capture on both species, Math. Methods Appl. Sci. 38(2015) 2876-2887], a mathematical model for a predator-prey model with general functional response and recruitment including capture on both species was formulated and analyzed. However, the global asymptotic stability (GAS) of this model was only partially resolved. In the present paper, we provide a rigorously mathematical analysis for the complete GAS of the predator-prey model. By using the Lyapunov stability theory in combination with some nonstandard techniques of mathematical analysis for dynamical systems, the GAS of equilibria of the model is determined fully. The obtained results not only provide an important improvement for the population dynamics of the predator-prey model but also can be extended to study its modified versions in the context of fractional-order derivatives. The theoretical results are supported and illustrated by a set of numerical examples.

Peer review status:UNDER REVIEW

28 Jul 2021Submitted to Mathematical Methods in the Applied Sciences
29 Jul 2021Assigned to Editor
29 Jul 2021Submission Checks Completed
02 Aug 2021Reviewer(s) Assigned