Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays
In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, we explore the stability region of the positive constant steady state by calculating the stability switching curves. Then we derive the Hopf and double Hopf bifurcation theorem via the crossi...
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doaj-69b231e2216f404bbe9073365cb1c6202021-04-02T19:46:58ZengVilnius University PressNonlinear Analysis1392-51132335-89632021-01-0126110.15388/namc.2021.26.20561Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delaysYuying Liu0Junjie Wei1Harbin Institute of TechnologyHarbin Institute of Technology, Jimei University In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, we explore the stability region of the positive constant steady state by calculating the stability switching curves. Then we derive the Hopf and double Hopf bifurcation theorem via the crossing directions of the stability switching curves. Moreover, we calculate the normal forms near the double Hopf singularities by taking two delays as parameters. We carry out some numerical simulations for illustrating the theoretical results. Both theoretical analysis and numerical simulation show that the system near double Hopf singularity has rich dynamics, including stable spatially homogeneous and inhomogeneous periodic solutions. Finally, we evaluate the influence of two parameters on the existence of double Hopf bifurcation. https://www.journals.vu.lt/nonlinear-analysis/article/view/20561predator–preystrong Allee effectdouble Hopf bifurcationtwo delaysstability switching curves |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yuying Liu Junjie Wei |
spellingShingle |
Yuying Liu Junjie Wei Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays Nonlinear Analysis predator–prey strong Allee effect double Hopf bifurcation two delays stability switching curves |
author_facet |
Yuying Liu Junjie Wei |
author_sort |
Yuying Liu |
title |
Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays |
title_short |
Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays |
title_full |
Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays |
title_fullStr |
Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays |
title_full_unstemmed |
Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays |
title_sort |
double hopf bifurcation of a diffusive predator–prey system with strong allee effect and two delays |
publisher |
Vilnius University Press |
series |
Nonlinear Analysis |
issn |
1392-5113 2335-8963 |
publishDate |
2021-01-01 |
description |
In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, we explore the stability region of the positive constant steady state by calculating the stability switching curves. Then we derive the Hopf and double Hopf bifurcation theorem via the crossing directions of the stability switching curves. Moreover, we calculate the normal forms near the double Hopf singularities by taking two delays as parameters. We carry out some numerical simulations for illustrating the theoretical results. Both theoretical analysis and numerical simulation show that the system near double Hopf singularity has rich dynamics, including stable spatially homogeneous and inhomogeneous periodic solutions. Finally, we evaluate the influence of two parameters on the existence of double Hopf bifurcation.
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topic |
predator–prey strong Allee effect double Hopf bifurcation two delays stability switching curves |
url |
https://www.journals.vu.lt/nonlinear-analysis/article/view/20561 |
work_keys_str_mv |
AT yuyingliu doublehopfbifurcationofadiffusivepredatorpreysystemwithstrongalleeeffectandtwodelays AT junjiewei doublehopfbifurcationofadiffusivepredatorpreysystemwithstrongalleeeffectandtwodelays |
_version_ |
1721548369246027776 |