Bifurcations on a discontinuous Leslie-Grower model with harvesting and alternative food for predators and Holling II functional response Articles uri icon

authors

  • CORTES GARCIA, CHRISTIAN CAMILO

publication date

  • August 2022

start page

  • 1

end page

  • 25

volume

  • 116

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.

subjects

  • Biology and Biomedicine
  • Mathematics

keywords

  • planar filippov systems; grazing bifurcation; limit cycle; pseudo-equilibrium; logistic growth