Spatiotemporal Dynamics of a Diffusive Predator–Prey System with Allee Effect and Threshold Hunting
Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non...
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| Autor*in: |
Wu, Daiyong [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of nonlinear science - Springer US, 1991, 30(2019), 3 vom: 22. Nov., Seite 1015-1054 |
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| Übergeordnetes Werk: |
volume:30 ; year:2019 ; number:3 ; day:22 ; month:11 ; pages:1015-1054 |
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| DOI / URN: |
10.1007/s00332-019-09600-0 |
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OLC2057911667 |
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| 520 | |a Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non-spatial system based on ordinary differential equations is presented. It is noted that four stable equilibrium points coexist due to the Allee effect and threshold hunting. The stability of interior equilibrium points and the existence of Turing instability induced by the diffusion, spatially homogeneous and inhomogeneous Hopf bifurcation, Turing–Hopf bifurcation are studied by analyzing the corresponding characteristic equation for spatial system. By constructing generalized Jacobian matrix, we analyze the stability of interior equilibrium point where u-component is equal to the threshold of functional response. These results show that the Allee effect, threshold hunting and diffusion have significant impacts on the dynamics. Last, we present some numerical simulations that supplement the analytic results. | ||
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10.1007/s00332-019-09600-0 doi (DE-627)OLC2057911667 (DE-He213)s00332-019-09600-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ 11 ssgn Wu, Daiyong verfasserin aut Spatiotemporal Dynamics of a Diffusive Predator–Prey System with Allee Effect and Threshold Hunting 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non-spatial system based on ordinary differential equations is presented. It is noted that four stable equilibrium points coexist due to the Allee effect and threshold hunting. The stability of interior equilibrium points and the existence of Turing instability induced by the diffusion, spatially homogeneous and inhomogeneous Hopf bifurcation, Turing–Hopf bifurcation are studied by analyzing the corresponding characteristic equation for spatial system. By constructing generalized Jacobian matrix, we analyze the stability of interior equilibrium point where u-component is equal to the threshold of functional response. These results show that the Allee effect, threshold hunting and diffusion have significant impacts on the dynamics. Last, we present some numerical simulations that supplement the analytic results. Reaction–diffusion Predator–prey system Allee effect Threshold hunting Turing–Hopf bifurcation Zhao, Hongyong (orcid)0000-0003-2286-9922 aut Enthalten in Journal of nonlinear science Springer US, 1991 30(2019), 3 vom: 22. Nov., Seite 1015-1054 (DE-627)130975990 (DE-600)1072984-7 (DE-576)025193295 0938-8974 nnns volume:30 year:2019 number:3 day:22 month:11 pages:1015-1054 https://doi.org/10.1007/s00332-019-09600-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 30 2019 3 22 11 1015-1054 |
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10.1007/s00332-019-09600-0 doi (DE-627)OLC2057911667 (DE-He213)s00332-019-09600-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ 11 ssgn Wu, Daiyong verfasserin aut Spatiotemporal Dynamics of a Diffusive Predator–Prey System with Allee Effect and Threshold Hunting 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non-spatial system based on ordinary differential equations is presented. It is noted that four stable equilibrium points coexist due to the Allee effect and threshold hunting. The stability of interior equilibrium points and the existence of Turing instability induced by the diffusion, spatially homogeneous and inhomogeneous Hopf bifurcation, Turing–Hopf bifurcation are studied by analyzing the corresponding characteristic equation for spatial system. By constructing generalized Jacobian matrix, we analyze the stability of interior equilibrium point where u-component is equal to the threshold of functional response. These results show that the Allee effect, threshold hunting and diffusion have significant impacts on the dynamics. Last, we present some numerical simulations that supplement the analytic results. Reaction–diffusion Predator–prey system Allee effect Threshold hunting Turing–Hopf bifurcation Zhao, Hongyong (orcid)0000-0003-2286-9922 aut Enthalten in Journal of nonlinear science Springer US, 1991 30(2019), 3 vom: 22. Nov., Seite 1015-1054 (DE-627)130975990 (DE-600)1072984-7 (DE-576)025193295 0938-8974 nnns volume:30 year:2019 number:3 day:22 month:11 pages:1015-1054 https://doi.org/10.1007/s00332-019-09600-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 30 2019 3 22 11 1015-1054 |
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10.1007/s00332-019-09600-0 doi (DE-627)OLC2057911667 (DE-He213)s00332-019-09600-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ 11 ssgn Wu, Daiyong verfasserin aut Spatiotemporal Dynamics of a Diffusive Predator–Prey System with Allee Effect and Threshold Hunting 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non-spatial system based on ordinary differential equations is presented. It is noted that four stable equilibrium points coexist due to the Allee effect and threshold hunting. The stability of interior equilibrium points and the existence of Turing instability induced by the diffusion, spatially homogeneous and inhomogeneous Hopf bifurcation, Turing–Hopf bifurcation are studied by analyzing the corresponding characteristic equation for spatial system. By constructing generalized Jacobian matrix, we analyze the stability of interior equilibrium point where u-component is equal to the threshold of functional response. These results show that the Allee effect, threshold hunting and diffusion have significant impacts on the dynamics. Last, we present some numerical simulations that supplement the analytic results. Reaction–diffusion Predator–prey system Allee effect Threshold hunting Turing–Hopf bifurcation Zhao, Hongyong (orcid)0000-0003-2286-9922 aut Enthalten in Journal of nonlinear science Springer US, 1991 30(2019), 3 vom: 22. Nov., Seite 1015-1054 (DE-627)130975990 (DE-600)1072984-7 (DE-576)025193295 0938-8974 nnns volume:30 year:2019 number:3 day:22 month:11 pages:1015-1054 https://doi.org/10.1007/s00332-019-09600-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 30 2019 3 22 11 1015-1054 |
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Spatiotemporal Dynamics of a Diffusive Predator–Prey System with Allee Effect and Threshold Hunting |
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Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non-spatial system based on ordinary differential equations is presented. It is noted that four stable equilibrium points coexist due to the Allee effect and threshold hunting. The stability of interior equilibrium points and the existence of Turing instability induced by the diffusion, spatially homogeneous and inhomogeneous Hopf bifurcation, Turing–Hopf bifurcation are studied by analyzing the corresponding characteristic equation for spatial system. By constructing generalized Jacobian matrix, we analyze the stability of interior equilibrium point where u-component is equal to the threshold of functional response. These results show that the Allee effect, threshold hunting and diffusion have significant impacts on the dynamics. Last, we present some numerical simulations that supplement the analytic results. © Springer Science+Business Media, LLC, part of Springer Nature 2019 |
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Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non-spatial system based on ordinary differential equations is presented. It is noted that four stable equilibrium points coexist due to the Allee effect and threshold hunting. The stability of interior equilibrium points and the existence of Turing instability induced by the diffusion, spatially homogeneous and inhomogeneous Hopf bifurcation, Turing–Hopf bifurcation are studied by analyzing the corresponding characteristic equation for spatial system. By constructing generalized Jacobian matrix, we analyze the stability of interior equilibrium point where u-component is equal to the threshold of functional response. These results show that the Allee effect, threshold hunting and diffusion have significant impacts on the dynamics. Last, we present some numerical simulations that supplement the analytic results. © Springer Science+Business Media, LLC, part of Springer Nature 2019 |
| abstract_unstemmed |
Abstract In this paper, we study a diffusive predator–prey system with the Allee effect and threshold hunting. First, the number of interior equilibrium points is determined by discussing the relation of parameters. Then, preliminary analysis on the local asymptotic stability and bifurcations of non-spatial system based on ordinary differential equations is presented. It is noted that four stable equilibrium points coexist due to the Allee effect and threshold hunting. The stability of interior equilibrium points and the existence of Turing instability induced by the diffusion, spatially homogeneous and inhomogeneous Hopf bifurcation, Turing–Hopf bifurcation are studied by analyzing the corresponding characteristic equation for spatial system. By constructing generalized Jacobian matrix, we analyze the stability of interior equilibrium point where u-component is equal to the threshold of functional response. These results show that the Allee effect, threshold hunting and diffusion have significant impacts on the dynamics. Last, we present some numerical simulations that supplement the analytic results. © Springer Science+Business Media, LLC, part of Springer Nature 2019 |
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| title_short |
Spatiotemporal Dynamics of a Diffusive Predator–Prey System with Allee Effect and Threshold Hunting |
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https://doi.org/10.1007/s00332-019-09600-0 |
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Zhao, Hongyong |
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