Stability and Hopf bifurcation of a predator-prey model

Abstract In this paper, we study a class of predator-prey model with Holling-II functional response. Firstly, by using linearization method, we prove the stability of nonnegative equilibrium points. Secondly, we obtain the existence, direction, and stability of Hopf bifurcation by using Poincare–And...

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Main Authors:	Fan Wu, Yujuan Jiao
Format:	Article
Language:	English
Published:	SpringerOpen 2019-07-01
Series:	Boundary Value Problems
Subjects:	Predator-prey model Stability Hopf bifurcation Poincare–Andronow Hopf bifurcation theorem
Online Access:	http://link.springer.com/article/10.1186/s13661-019-1242-9

id	doaj-1c189c24a3c248759a808ab300ab9680
record_format	Article
spelling	doaj-1c189c24a3c248759a808ab300ab96802020-11-25T03:02:28ZengSpringerOpenBoundary Value Problems1687-27702019-07-012019111110.1186/s13661-019-1242-9Stability and Hopf bifurcation of a predator-prey modelFan Wu0Yujuan Jiao1College of Mathematics and Computer Science, Northwest Minzu UniversityCollege of Mathematics and Computer Science, Northwest Minzu UniversityAbstract In this paper, we study a class of predator-prey model with Holling-II functional response. Firstly, by using linearization method, we prove the stability of nonnegative equilibrium points. Secondly, we obtain the existence, direction, and stability of Hopf bifurcation by using Poincare–Andronov Hopf bifurcation theorem. Finally, we demonstrate the validity of our results by numerical simulation.http://link.springer.com/article/10.1186/s13661-019-1242-9Predator-prey modelStabilityHopf bifurcationPoincare–Andronow Hopf bifurcation theorem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Fan Wu Yujuan Jiao
spellingShingle	Fan Wu Yujuan Jiao Stability and Hopf bifurcation of a predator-prey model Boundary Value Problems Predator-prey model Stability Hopf bifurcation Poincare–Andronow Hopf bifurcation theorem
author_facet	Fan Wu Yujuan Jiao
author_sort	Fan Wu
title	Stability and Hopf bifurcation of a predator-prey model
title_short	Stability and Hopf bifurcation of a predator-prey model
title_full	Stability and Hopf bifurcation of a predator-prey model
title_fullStr	Stability and Hopf bifurcation of a predator-prey model
title_full_unstemmed	Stability and Hopf bifurcation of a predator-prey model
title_sort	stability and hopf bifurcation of a predator-prey model
publisher	SpringerOpen
series	Boundary Value Problems
issn	1687-2770
publishDate	2019-07-01
description	Abstract In this paper, we study a class of predator-prey model with Holling-II functional response. Firstly, by using linearization method, we prove the stability of nonnegative equilibrium points. Secondly, we obtain the existence, direction, and stability of Hopf bifurcation by using Poincare–Andronov Hopf bifurcation theorem. Finally, we demonstrate the validity of our results by numerical simulation.
topic	Predator-prey model Stability Hopf bifurcation Poincare–Andronow Hopf bifurcation theorem
url	http://link.springer.com/article/10.1186/s13661-019-1242-9
work_keys_str_mv	AT fanwu stabilityandhopfbifurcationofapredatorpreymodel AT yujuanjiao stabilityandhopfbifurcationofapredatorpreymodel
_version_	1724689370992082944

Stability and Hopf bifurcation of a predator-prey model

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