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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.
@article{M2AN_2003__37_2_339_0,
author = {Mukherjee, Debasis},
title = {Persistence and bifurcation analysis on a predator-prey system of holling type},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {339--344},
publisher = {EDP-Sciences},
volume = {37},
number = {2},
year = {2003},
doi = {10.1051/m2an:2003029},
zbl = {1029.34040},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003029/}
}
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 PY - 2003 SP - 339 EP - 344 VL - 37 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003029/ DO - 10.1051/m2an:2003029 LA - en ID - M2AN_2003__37_2_339_0 ER -
%0 Journal Article %A Mukherjee, Debasis %T Persistence and bifurcation analysis on a predator-prey system of holling type %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2003 %P 339-344 %V 37 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003029/ %R 10.1051/m2an:2003029 %G en %F M2AN_2003__37_2_339_0
Mukherjee, Debasis. Persistence and bifurcation analysis on a predator-prey system of holling type. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 2, pp. 339-344. doi: 10.1051/m2an:2003029
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