Bifurcations on a discontinuous Leslie-Grower model with harvesting and alternative food for predators and Holling II functional response Articles
Overview
published in
publication date
- August 2022
start page
- 1
end page
- 25
volume
- 116
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 1007-5704
Electronic International Standard Serial Number (EISSN)
- 1878-7274
abstract
-
This paper proposes a mathematical model that describes the interaction of prey and
predators, assuming logistic growth for both species, harvesting and alternative food
for predators and functional response of the Holling II predator. When performing a
qualitative analysis to determine conditions in the parameters that allow the possible
extinction or preservation of prey and/or predators, a modification of the initial model is
made considering that the consumption of prey by predators is restricted if the amount
of prey is less than a critical value, whose dynamics is formulated by a planar Filippov
system. The study of the discontinuous model is carried out by bifurcation analysis in
relation to two parameters: harvesting of predators and critical value of prey.
Classification
subjects
- Biology and Biomedicine
- Mathematics
keywords
- planar filippov systems; grazing bifurcation; limit cycle; pseudo-equilibrium; logistic growth