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| Format: | Artículo científico |
| Sprache: | en |
| Veröffentlicht: |
Vilniaus Universitetas
2021
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| Online-Zugang: | https://www.redalyc.org/articulo.oa?id=694172828005 https://www.redalyc.org/journal/6941/694172828005/ https://www.redalyc.org/journal/6941/694172828005/html/ https://www.redalyc.org/journal/6941/694172828005/694172828005.epub https://www.redalyc.org/journal/6941/694172828005/movil https://doi.org/10.15388/namc.2021.26.20561 |
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| _version_ | 1866816400317743104 |
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| author | Liu Yuying |
| author_facet | Liu Yuying |
| contents | Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays Liu Yuying Weia Junjie Matemáticas prey Predator two delays strong Allee effect double Hopf bifurcation 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. 2021 artículo científico 1392-5113 https://www.redalyc.org/articulo.oa?id=694172828005 https://www.redalyc.org/journal/6941/694172828005/ https://www.redalyc.org/journal/6941/694172828005/html/ https://www.redalyc.org/journal/6941/694172828005/694172828005.epub https://www.redalyc.org/journal/6941/694172828005/movil https://doi.org/10.15388/namc.2021.26.20561 en http://www.redalyc.org/revista.oa?id=6941 Nonlinear Analysis: Modelling and Control application/pdf Vilniaus Universitetas Nonlinear Analysis: Modelling and Control (Lituania) Num.1 Vol.26 |
| format | Artículo científico |
| id | redalyc_694172828005 |
| language | en |
| publishDate | 2021 |
| publisher | Vilniaus Universitetas |
| spellingShingle | Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays Liu Yuying Matemáticas prey Predator two delays strong Allee effect double Hopf bifurcation Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays Liu Yuying Weia Junjie Matemáticas prey Predator two delays strong Allee effect double Hopf bifurcation 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. 2021 artículo científico 1392-5113 https://www.redalyc.org/articulo.oa?id=694172828005 https://www.redalyc.org/journal/6941/694172828005/ https://www.redalyc.org/journal/6941/694172828005/html/ https://www.redalyc.org/journal/6941/694172828005/694172828005.epub https://www.redalyc.org/journal/6941/694172828005/movil https://doi.org/10.15388/namc.2021.26.20561 en http://www.redalyc.org/revista.oa?id=6941 Nonlinear Analysis: Modelling and Control application/pdf Vilniaus Universitetas Nonlinear Analysis: Modelling and Control (Lituania) Num.1 Vol.26 |
| title | Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays |
| topic | Matemáticas prey Predator two delays strong Allee effect double Hopf bifurcation |
| url | https://www.redalyc.org/articulo.oa?id=694172828005 https://www.redalyc.org/journal/6941/694172828005/ https://www.redalyc.org/journal/6941/694172828005/html/ https://www.redalyc.org/journal/6941/694172828005/694172828005.epub https://www.redalyc.org/journal/6941/694172828005/movil https://doi.org/10.15388/namc.2021.26.20561 |