Spatial Nonhomogeneous Periodic Solutions Induced by Nonlocal Prey Competition in a Diffusive Predator-Prey Model

Shanshan Chen; Junjie Wei; Kaiqi Yang

doi:10.1142/S0218127419500433

Spatial Nonhomogeneous Periodic Solutions Induced by Nonlocal Prey Competition in a Diffusive Predator-Prey Model

Shanshan Chen^*
, Junjie Wei
, Kaiqi Yang

^*Corresponding author for this work

Harbin Institute of Technology Weihai
Foshan University

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

18 Scopus citations

Abstract

The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatially nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state may lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values could be spatially nonhomogeneous and orbitally asymptotically stable.

Original language	English
Article number	1950043
Journal	International Journal of Bifurcation and Chaos
Volume	29
Issue number	4
DOIs	https://doi.org/10.1142/S0218127419500433
State	Published - 1 Apr 2019
Externally published	Yes

Keywords

Hopf bifurcation
Predator-prey model
nonlocal competition
spatially nonhomogeneous periodic solutions

Access to Document

10.1142/S0218127419500433

Cite this

@article{b320635b85414bb38619235f6f09f138,

title = "Spatial Nonhomogeneous Periodic Solutions Induced by Nonlocal Prey Competition in a Diffusive Predator-Prey Model",

abstract = "The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatially nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state may lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values could be spatially nonhomogeneous and orbitally asymptotically stable.",

keywords = "Hopf bifurcation, Predator-prey model, nonlocal competition, spatially nonhomogeneous periodic solutions",

author = "Shanshan Chen and Junjie Wei and Kaiqi Yang",

note = "Publisher Copyright: {\textcopyright} 2019 World Scientific Publishing Company.",

year = "2019",

month = apr,

day = "1",

doi = "10.1142/S0218127419500433",

language = "英语",

volume = "29",

journal = "International Journal of Bifurcation and Chaos",

issn = "0218-1274",

publisher = "World Scientific",

number = "4",

}

TY - JOUR

T1 - Spatial Nonhomogeneous Periodic Solutions Induced by Nonlocal Prey Competition in a Diffusive Predator-Prey Model

AU - Chen, Shanshan

AU - Wei, Junjie

AU - Yang, Kaiqi

PY - 2019/4/1

Y1 - 2019/4/1

N2 - The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatially nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state may lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values could be spatially nonhomogeneous and orbitally asymptotically stable.

AB - The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatially nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state may lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values could be spatially nonhomogeneous and orbitally asymptotically stable.

KW - Hopf bifurcation

KW - Predator-prey model

KW - nonlocal competition

KW - spatially nonhomogeneous periodic solutions

UR - https://www.scopus.com/pages/publications/85064719292

U2 - 10.1142/S0218127419500433

DO - 10.1142/S0218127419500433

M3 - 文章

AN - SCOPUS:85064719292

SN - 0218-1274

VL - 29

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 4

M1 - 1950043

ER -

Spatial Nonhomogeneous Periodic Solutions Induced by Nonlocal Prey Competition in a Diffusive Predator-Prey Model

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this