Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth

Abstract In this paper, we study a diffusion Holling–Tanner predator–prey model with ratio-dependent functional response and Simth growth subject to a homogeneous Neumann boundary condition. Firstly, we use iteration technique and eigenvalue analysis to get the local stability and a Hopf bifurcation...

Full description

Bibliographic Details
Main Authors:	Huiping Fang, Ling Hu, Yongfeng Wu
Format:	Article
Language:	English
Published:	SpringerOpen 2018-08-01
Series:	Advances in Difference Equations
Subjects:	Diffusion Delay Simth growth Positive equilibrium Hopf bifurcation
Online Access:	http://link.springer.com/article/10.1186/s13662-018-1726-4

id	doaj-af93e7b98b3c4e8f98b1516e4061ebff
record_format	Article
spelling	doaj-af93e7b98b3c4e8f98b1516e4061ebff2020-11-25T01:56:14ZengSpringerOpenAdvances in Difference Equations1687-18472018-08-012018111110.1186/s13662-018-1726-4Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growthHuiping Fang0Ling Hu1Yongfeng Wu2School of Mathematics and Statistics, Huangshan UniversitySchool of Mathematics and Statistics, Huangshan UniversitySchool of Mathematics and Finance, Chuzhou UniversityAbstract In this paper, we study a diffusion Holling–Tanner predator–prey model with ratio-dependent functional response and Simth growth subject to a homogeneous Neumann boundary condition. Firstly, we use iteration technique and eigenvalue analysis to get the local stability and a Hopf bifurcation at the positive equilibrium. Secondly, by choosing the constant related to delay as bifurcation parameter we obtain periodic solutions near the positive equilibrium. Besides, by using center manifold theory and normal form theory we reflect the stability with Hopf bifurcating periodic solution and bifurcating direction.http://link.springer.com/article/10.1186/s13662-018-1726-4DiffusionDelaySimth growthPositive equilibriumHopf bifurcation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Huiping Fang Ling Hu Yongfeng Wu
spellingShingle	Huiping Fang Ling Hu Yongfeng Wu Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth Advances in Difference Equations Diffusion Delay Simth growth Positive equilibrium Hopf bifurcation
author_facet	Huiping Fang Ling Hu Yongfeng Wu
author_sort	Huiping Fang
title	Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth
title_short	Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth
title_full	Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth
title_fullStr	Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth
title_full_unstemmed	Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth
title_sort	delay-induced hopf bifurcation in a diffusive holling–tanner predator–prey model with ratio-dependent response and smith growth
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2018-08-01
description	Abstract In this paper, we study a diffusion Holling–Tanner predator–prey model with ratio-dependent functional response and Simth growth subject to a homogeneous Neumann boundary condition. Firstly, we use iteration technique and eigenvalue analysis to get the local stability and a Hopf bifurcation at the positive equilibrium. Secondly, by choosing the constant related to delay as bifurcation parameter we obtain periodic solutions near the positive equilibrium. Besides, by using center manifold theory and normal form theory we reflect the stability with Hopf bifurcating periodic solution and bifurcating direction.
topic	Diffusion Delay Simth growth Positive equilibrium Hopf bifurcation
url	http://link.springer.com/article/10.1186/s13662-018-1726-4
work_keys_str_mv	AT huipingfang delayinducedhopfbifurcationinadiffusivehollingtannerpredatorpreymodelwithratiodependentresponseandsmithgrowth AT linghu delayinducedhopfbifurcationinadiffusivehollingtannerpredatorpreymodelwithratiodependentresponseandsmithgrowth AT yongfengwu delayinducedhopfbifurcationinadiffusivehollingtannerpredatorpreymodelwithratiodependentresponseandsmithgrowth
_version_	1724980715646353408

Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth

Similar Items