Zero singularities of codimension two in a delayed predator-prey diffusion system

Jinling Wang; Jinling Liang; Yurong Liu; Jin Liang Wang

doi:10.1016/j.neucom.2016.07.060

Zero singularities of codimension two in a delayed predator-prey diffusion system

Jinling Wang
, Jinling Liang^*
, Yurong Liu
, Jin Liang Wang

^*Corresponding author for this work

Southeast University, Nanjing
Yangzhou University
King Abdulaziz University
Tiangong University

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

3 Scopus citations

Abstract

In this paper, a delayed predator-prey diffusion system with Neumann boundary condition is addressed. By complex computation and rigorous analysis, it is obtained that the unique positive equilibrium of the system under consideration is a Bogdanov-Takens (B-T) singularity under certain conditions, whereas this is not true for the corresponding system without diffusion. By using the normal form theory and the center manifold reduction theorem for partial functional differential equations (PFDEs), the normal form of the B-T singularity is provided. Finally, numerical simulations are carried out to illustrate the theoretical results presented.

Original language	English
Pages (from-to)	10-17
Number of pages	8
Journal	Neurocomputing
Volume	227
DOIs	https://doi.org/10.1016/j.neucom.2016.07.060
State	Published - 1 Mar 2017
Externally published	Yes

Keywords

Bogdanov-Takens (B-T) bifurcation
Diffusion
Predator-prey system
Time delay

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10.1016/j.neucom.2016.07.060

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title = "Zero singularities of codimension two in a delayed predator-prey diffusion system",

abstract = "In this paper, a delayed predator-prey diffusion system with Neumann boundary condition is addressed. By complex computation and rigorous analysis, it is obtained that the unique positive equilibrium of the system under consideration is a Bogdanov-Takens (B-T) singularity under certain conditions, whereas this is not true for the corresponding system without diffusion. By using the normal form theory and the center manifold reduction theorem for partial functional differential equations (PFDEs), the normal form of the B-T singularity is provided. Finally, numerical simulations are carried out to illustrate the theoretical results presented.",

keywords = "Bogdanov-Takens (B-T) bifurcation, Diffusion, Predator-prey system, Time delay",

author = "Jinling Wang and Jinling Liang and Yurong Liu and Wang, \{Jin Liang\}",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2017",

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day = "1",

doi = "10.1016/j.neucom.2016.07.060",

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TY - JOUR

T1 - Zero singularities of codimension two in a delayed predator-prey diffusion system

AU - Wang, Jinling

AU - Liang, Jinling

AU - Liu, Yurong

AU - Wang, Jin Liang

PY - 2017/3/1

Y1 - 2017/3/1

N2 - In this paper, a delayed predator-prey diffusion system with Neumann boundary condition is addressed. By complex computation and rigorous analysis, it is obtained that the unique positive equilibrium of the system under consideration is a Bogdanov-Takens (B-T) singularity under certain conditions, whereas this is not true for the corresponding system without diffusion. By using the normal form theory and the center manifold reduction theorem for partial functional differential equations (PFDEs), the normal form of the B-T singularity is provided. Finally, numerical simulations are carried out to illustrate the theoretical results presented.

AB - In this paper, a delayed predator-prey diffusion system with Neumann boundary condition is addressed. By complex computation and rigorous analysis, it is obtained that the unique positive equilibrium of the system under consideration is a Bogdanov-Takens (B-T) singularity under certain conditions, whereas this is not true for the corresponding system without diffusion. By using the normal form theory and the center manifold reduction theorem for partial functional differential equations (PFDEs), the normal form of the B-T singularity is provided. Finally, numerical simulations are carried out to illustrate the theoretical results presented.

KW - Bogdanov-Takens (B-T) bifurcation

KW - Diffusion

KW - Predator-prey system

KW - Time delay

UR - https://www.scopus.com/pages/publications/85007613562

U2 - 10.1016/j.neucom.2016.07.060

DO - 10.1016/j.neucom.2016.07.060

M3 - 文章

AN - SCOPUS:85007613562

SN - 0925-2312

VL - 227

SP - 10

EP - 17

JO - Neurocomputing

JF - Neurocomputing

ER -

Zero singularities of codimension two in a delayed predator-prey diffusion system

Abstract

Keywords

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