Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect
In this paper, a delayed diffusive predator–prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive...
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Online Access: | http://dx.doi.org/10.1080/17513758.2020.1850892 |
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doaj-16ef4c03800d449e82a082d8072bd5352020-12-07T17:17:41ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662020-01-0114182684810.1080/17513758.2020.18508921850892Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effectXin-You Meng0Jiao-Guo Wang1Lanzhou University of TechnologyLanzhou University of TechnologyIn this paper, a delayed diffusive predator–prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained. In addition, the local stability of the coexistent equilibrium and existence of Hopf bifurcation of system with time delay are discussed. Moreover, the properties of Hopf bifurcation are studied based on the centre manifold and normal form theory for partial functional differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical results.http://dx.doi.org/10.1080/17513758.2020.1850892schooling behaviourtime delayhopf bifurcationpredator–preyallee effect |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xin-You Meng Jiao-Guo Wang |
spellingShingle |
Xin-You Meng Jiao-Guo Wang Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect Journal of Biological Dynamics schooling behaviour time delay hopf bifurcation predator–prey allee effect |
author_facet |
Xin-You Meng Jiao-Guo Wang |
author_sort |
Xin-You Meng |
title |
Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect |
title_short |
Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect |
title_full |
Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect |
title_fullStr |
Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect |
title_full_unstemmed |
Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect |
title_sort |
dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and allee effect |
publisher |
Taylor & Francis Group |
series |
Journal of Biological Dynamics |
issn |
1751-3758 1751-3766 |
publishDate |
2020-01-01 |
description |
In this paper, a delayed diffusive predator–prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained. In addition, the local stability of the coexistent equilibrium and existence of Hopf bifurcation of system with time delay are discussed. Moreover, the properties of Hopf bifurcation are studied based on the centre manifold and normal form theory for partial functional differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical results. |
topic |
schooling behaviour time delay hopf bifurcation predator–prey allee effect |
url |
http://dx.doi.org/10.1080/17513758.2020.1850892 |
work_keys_str_mv |
AT xinyoumeng dynamicalanalysisofadelayeddiffusivepredatorpreymodelwithschoolingbehaviourandalleeeffect AT jiaoguowang dynamicalanalysisofadelayeddiffusivepredatorpreymodelwithschoolingbehaviourandalleeeffect |
_version_ |
1724397458714263552 |