Persistence and bifurcation analysis on a predator-prey system of holling type
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 2, p. 339-344

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.

DOI : https://doi.org/10.1051/m2an:2003029
Classification:  34D23,  34D45,  92D25
Keywords: persistance, bifurcation, stability, holling type II
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {37},
number = {2},
year = {2003},
pages = {339-344},
doi = {10.1051/m2an:2003029},
zbl = {1029.34040},
language = {en},
url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 2, pp. 339-344. doi : 10.1051/m2an:2003029. http://www.numdam.org/item/M2AN_2003__37_2_339_0/

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