# On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay

Mathematical Modelling of Natural Phenomena (2009)

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

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topRuan, 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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