On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay

S. Ruan

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 2, page 140-188
  • ISSN: 0973-5348

Abstract

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In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations in delayed predator-prey models with nonmonotone functional response and in delayed predator-prey model with predator harvesting are also introduced.

How to cite

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Ruan, S.. "On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay." Mathematical Modelling of Natural Phenomena 4.2 (2009): 140-188. <http://eudml.org/doc/222306>.

@article{Ruan2009,
abstract = { In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations in delayed predator-prey models with nonmonotone functional response and in delayed predator-prey model with predator harvesting are also introduced. },
author = {Ruan, S.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {predator-prey model; time delay; harvesting; stability; bifurcation; predator-prey delayed model; bifurcations},
language = {eng},
month = {3},
number = {2},
pages = {140-188},
publisher = {EDP Sciences},
title = {On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay},
url = {http://eudml.org/doc/222306},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Ruan, S.
TI - On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/3//
PB - EDP Sciences
VL - 4
IS - 2
SP - 140
EP - 188
AB - In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations in delayed predator-prey models with nonmonotone functional response and in delayed predator-prey model with predator harvesting are also introduced.
LA - eng
KW - predator-prey model; time delay; harvesting; stability; bifurcation; predator-prey delayed model; bifurcations
UR - http://eudml.org/doc/222306
ER -

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