Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity
Abstract In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-01-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-020-03161-3 |
| _version_ | 1818427810553790464 |
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| author | Ruizhi Yang Yuxin Ma Chiyu Zhang |
| author_facet | Ruizhi Yang Yuxin Ma Chiyu Zhang |
| author_sort | Ruizhi Yang |
| collection | DOAJ |
| description | Abstract In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial functional differential equations, the formulas for determining the property of Hopf bifurcation are given. |
| first_indexed | 2024-12-14T14:51:39Z |
| format | Article |
| id | doaj.art-93ee2d0f165149649b07da7197aebff0 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T14:51:39Z |
| publishDate | 2021-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-93ee2d0f165149649b07da7197aebff02022-12-21T22:57:07ZengSpringerOpenAdvances in Difference Equations1687-18472021-01-012021111710.1186/s13662-020-03161-3Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicityRuizhi Yang0Yuxin Ma1Chiyu Zhang2Department of Mathematics, Northeast Forestry UniversityDepartment of Mathematics, Northeast Forestry UniversityDepartment of Mathematics, Northeast Forestry UniversityAbstract In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial functional differential equations, the formulas for determining the property of Hopf bifurcation are given.https://doi.org/10.1186/s13662-020-03161-3Predator–preyDelayStabilityHopf bifurcation |
| spellingShingle | Ruizhi Yang Yuxin Ma Chiyu Zhang Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity Advances in Difference Equations Predator–prey Delay Stability Hopf bifurcation |
| title | Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity |
| title_full | Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity |
| title_fullStr | Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity |
| title_full_unstemmed | Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity |
| title_short | Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity |
| title_sort | time delay induced hopf bifurcation in a diffusive predator prey model with prey toxicity |
| topic | Predator–prey Delay Stability Hopf bifurcation |
| url | https://doi.org/10.1186/s13662-020-03161-3 |
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