Effect of fear and non-linear predator harvesting on a predator–prey system in presence of environmental variability

In this paper, we have proposed and analyzed a predator–prey system introducing the cost of predation fear into the prey reproduction with Holling type-II functional response in the stochastic environment with the consideration of non-linear harvesting on predators. The system experiences Transcriti...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics and computers in simulation 2025-01, Vol.227, p.442-460
Main Authors: Paul, Biswajit, Sikdar, Gopal Chandra, Ghosh, Uttam
Format: Article
Language:English
Subjects:
Density function
Fear effect
Hopf and Bogdanov–Takens bifurcation
Prey-predator model
Stationary distribution
Stochastic environment
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we have proposed and analyzed a predator–prey system introducing the cost of predation fear into the prey reproduction with Holling type-II functional response in the stochastic environment with the consideration of non-linear harvesting on predators. The system experiences Transcritical, Saddle–node, Hopf, and Bogdanov-Taken (BT) bifurcation with respect to the intrinsic growth rate and competition rate of the prey populations. We have discussed the existence and uniqueness of positive global solution of the stochastic model with the help of Ito’s integral formula and the long-term behavior of the solution is derived here. The existence of stationary distribution and explicit form of the density function is established here when only prey populations survive or both populations. We have shown that due to high fluctuation, the regime changes from one stable state to another state when bistability occurs in the system. The paper ends with some conclusions.
ISSN:0378-4754
DOI:10.1016/j.matcom.2024.08.021