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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-06-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03437-2 |
| _version_ | 1818640959540297728 |
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| author | Assane Savadogo Boureima Sangaré Hamidou Ouedraogo |
| author_facet | Assane Savadogo Boureima Sangaré Hamidou Ouedraogo |
| author_sort | Assane Savadogo |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-16T23:19:33Z |
| format | Article |
| id | doaj.art-13d22c33a0494c518b7f3c0ae5b91769 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T23:19:33Z |
| publishDate | 2021-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-13d22c33a0494c518b7f3c0ae5b917692022-12-21T22:12:11ZengSpringerOpenAdvances 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 |
| 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 |
| title | 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_short | 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 |
| topic | Prey-predator system Hopf-bifurcation Global stability Numerical simulations |
| url | https://doi.org/10.1186/s13662-021-03437-2 |
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