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Bifurcation and optimal harvesting analysis of a discrete-time predator–prey model with fear and prey refuge effects.

Authors :
Liu, Jie
Wang, Qinglong
Cao, Xuyang
Yu, Ting
Source :
AIMS Mathematics; 2024, Vol. 9 Issue 10, p1-24, 24p
Publication Year :
2024

Abstract

In this contribution, the complicated dynamical behaviors and optimal harvesting policy of a discrete-time predator–prey model with fear and refuge effects are formulated. Both the fear and prey refuge effects refer to an interaction between predator and prey. In the first place, the existence and local stability of three fixed points of proposed model are investigated by virtue of our methodology, that is, the eigenvalues of the Jacobian matrix. One step further, it is worth mentioning that the model undergoes flip bifurcation (i.e., period–doubling bifurcation) and Neimark–Sacker bifurcation at the interior fixed point by the utilization of bifurcation theory and center manifold theory. Also, optimal harvesting strategy is investigated, and the expressions of optimal harvesting efforts are determined. Two examples, in the end, are put forward to prove that they are consistent with the previous theoretical results. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
24736988
Volume :
9
Issue :
10
Database :
Complementary Index
Journal :
AIMS Mathematics
Publication Type :
Academic Journal
Accession number :
180607492
Full Text :
https://doi.org/10.3934/math.20241281