Allee effects in a Ricker-type predator-prey system

Yunshyong Chow; Sophia R.J. Jang

doi:10.1080/10236198.2014.918966

Allee effects in a Ricker-type predator-prey system

Yunshyong Chow, Sophia R.J. Jang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We study a discrete host-parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host-parasitoid interaction are completely analysed. If the host's intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.

Original language	English
Pages (from-to)	1350-1371
Number of pages	22
Journal	Journal of Difference Equations and Applications
Volume	20
Issue number	9
DOIs	https://doi.org/10.1080/10236198.2014.918966
State	Published - Sep 2014

Keywords

Allee effects
Ricker model
linear stability
period-doubling bifurcation

Access to Document

10.1080/10236198.2014.918966

Cite this

@article{fa6c4a28b96b4419aebf0e771141ae02,

title = "Allee effects in a Ricker-type predator-prey system",

abstract = "We study a discrete host-parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host-parasitoid interaction are completely analysed. If the host's intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.",

keywords = "Allee effects, Ricker model, linear stability, period-doubling bifurcation",

author = "Yunshyong Chow and Jang, {Sophia R.J.}",

note = "Funding Information: We thank both referees for their valuable comments and suggestions. Y. Chow acknowledges the support of the National Science Council of Taiwan. S. Jang thanks the Institute of Mathematics, Academia Sinica, Taiwan for its financial and staff support for her winter 2012 and summer 2013 visits.",

year = "2014",

month = sep,

doi = "10.1080/10236198.2014.918966",

language = "English",

volume = "20",

pages = "1350--1371",

journal = "Journal of Difference Equations and Applications",

issn = "1023-6198",

number = "9",

}

TY - JOUR

T1 - Allee effects in a Ricker-type predator-prey system

AU - Chow, Yunshyong

AU - Jang, Sophia R.J.

N1 - Funding Information: We thank both referees for their valuable comments and suggestions. Y. Chow acknowledges the support of the National Science Council of Taiwan. S. Jang thanks the Institute of Mathematics, Academia Sinica, Taiwan for its financial and staff support for her winter 2012 and summer 2013 visits.

PY - 2014/9

Y1 - 2014/9

N2 - We study a discrete host-parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host-parasitoid interaction are completely analysed. If the host's intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.

AB - We study a discrete host-parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host-parasitoid interaction are completely analysed. If the host's intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.

KW - Allee effects

KW - Ricker model

KW - linear stability

KW - period-doubling bifurcation

UR - http://www.scopus.com/inward/record.url?scp=84903608502&partnerID=8YFLogxK

U2 - 10.1080/10236198.2014.918966

DO - 10.1080/10236198.2014.918966

M3 - Article

AN - SCOPUS:84903608502

SN - 1023-6198

VL - 20

SP - 1350

EP - 1371

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 9

ER -

Allee effects in a Ricker-type predator-prey system

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this