A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response

Abstract In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solut...

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Main Authors: Assane Savadogo, Boureima Sangaré, Hamidou Ouedraogo
Format: Article
Language:English
Published: SpringerOpen 2021-06-01
Series:Advances in Difference Equations
Subjects:
Prey-predator system
Hopf-bifurcation
Global stability
Numerical simulations
Online Access:https://doi.org/10.1186/s13662-021-03437-2
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spelling doaj-13d22c33a0494c518b7f3c0ae5b917692021-06-06T11:45:48ZengSpringerOpenAdvances in Difference Equations1687-18472021-06-012021112310.1186/s13662-021-03437-2A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional responseAssane Savadogo0Boureima Sangaré1Hamidou Ouedraogo2Department of Mathematics and Informatics, UFR/ST, UNBDepartment of Mathematics and Informatics, UFR/ST, UNBDepartment of Mathematics and Informatics, UNBAbstract In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.https://doi.org/10.1186/s13662-021-03437-2Prey-predator systemHopf-bifurcationGlobal stabilityNumerical simulations
collection DOAJ
language English
format Article
sources DOAJ
author Assane Savadogo
Boureima Sangaré
Hamidou Ouedraogo
spellingShingle Assane Savadogo
Boureima Sangaré
Hamidou Ouedraogo
A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
Advances in Difference Equations
Prey-predator system
Hopf-bifurcation
Global stability
Numerical simulations
author_facet Assane Savadogo
Boureima Sangaré
Hamidou Ouedraogo
author_sort Assane Savadogo
title A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
title_short A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
title_full A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
title_fullStr A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
title_full_unstemmed A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
title_sort mathematical analysis of hopf-bifurcation in a prey-predator model with nonlinear functional response
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-06-01
description Abstract In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.
topic Prey-predator system
Hopf-bifurcation
Global stability
Numerical simulations
url https://doi.org/10.1186/s13662-021-03437-2
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AT boureimasangare amathematicalanalysisofhopfbifurcationinapreypredatormodelwithnonlinearfunctionalresponse
AT hamidououedraogo amathematicalanalysisofhopfbifurcationinapreypredatormodelwithnonlinearfunctionalresponse
AT assanesavadogo mathematicalanalysisofhopfbifurcationinapreypredatormodelwithnonlinearfunctionalresponse
AT boureimasangare mathematicalanalysisofhopfbifurcationinapreypredatormodelwithnonlinearfunctionalresponse
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