Persistence and bifurcation analysis on a predator–prey system of holling type

Debasis Mukherjee

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 2, page 339-344
  • ISSN: 0764-583X

Abstract

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We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.

How to cite

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Mukherjee, Debasis. "Persistence and bifurcation analysis on a predator–prey system of holling type." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 339-344. <http://eudml.org/doc/194166>.

@article{Mukherjee2010,
abstract = { We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation. },
author = {Mukherjee, Debasis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Persistance; bifurcation; stability; holling type II.; persistence; Holling type II},
language = {eng},
month = {3},
number = {2},
pages = {339-344},
publisher = {EDP Sciences},
title = {Persistence and bifurcation analysis on a predator–prey system of holling type},
url = {http://eudml.org/doc/194166},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Mukherjee, Debasis
TI - Persistence and bifurcation analysis on a predator–prey system of holling type
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 339
EP - 344
AB - We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.
LA - eng
KW - Persistance; bifurcation; stability; holling type II.; persistence; Holling type II
UR - http://eudml.org/doc/194166
ER -

References

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