Further investigations into the stability and bifurcation of a discrete predator–prey model
In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained i...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wang, Cheng [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015transfer abstract |
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| Schlagwörter: |
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| Umfang: |
20 |
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| Übergeordnetes Werk: |
Enthalten in: In silico drug repurposing in COVID-19: A network-based analysis - Sibilio, Pasquale ELSEVIER, 2021, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:422 ; year:2015 ; number:2 ; day:15 ; month:02 ; pages:920-939 ; extent:20 |
| Links: |
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| DOI / URN: |
10.1016/j.jmaa.2014.08.058 |
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| 520 | |a In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. | ||
| 520 | |a In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. | ||
| 650 | 7 | |a Discrete predator–prey model |2 Elsevier | |
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| 650 | 7 | |a Fold bifurcation |2 Elsevier | |
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10.1016/j.jmaa.2014.08.058 doi GBVA2015022000019.pica (DE-627)ELV01894518X (ELSEVIER)S0022-247X(14)00810-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 44.40 bkl Wang, Cheng verfasserin aut Further investigations into the stability and bifurcation of a discrete predator–prey model 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. Discrete predator–prey model Elsevier Project Method Elsevier Flip bifurcation Elsevier Fold bifurcation Elsevier Center Manifold Theorem Elsevier Li, Xianyi oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:422 year:2015 number:2 day:15 month:02 pages:920-939 extent:20 https://doi.org/10.1016/j.jmaa.2014.08.058 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 422 2015 2 15 0215 920-939 20 045F 510 |
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10.1016/j.jmaa.2014.08.058 doi GBVA2015022000019.pica (DE-627)ELV01894518X (ELSEVIER)S0022-247X(14)00810-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 44.40 bkl Wang, Cheng verfasserin aut Further investigations into the stability and bifurcation of a discrete predator–prey model 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. Discrete predator–prey model Elsevier Project Method Elsevier Flip bifurcation Elsevier Fold bifurcation Elsevier Center Manifold Theorem Elsevier Li, Xianyi oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:422 year:2015 number:2 day:15 month:02 pages:920-939 extent:20 https://doi.org/10.1016/j.jmaa.2014.08.058 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 422 2015 2 15 0215 920-939 20 045F 510 |
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10.1016/j.jmaa.2014.08.058 doi GBVA2015022000019.pica (DE-627)ELV01894518X (ELSEVIER)S0022-247X(14)00810-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 44.40 bkl Wang, Cheng verfasserin aut Further investigations into the stability and bifurcation of a discrete predator–prey model 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. Discrete predator–prey model Elsevier Project Method Elsevier Flip bifurcation Elsevier Fold bifurcation Elsevier Center Manifold Theorem Elsevier Li, Xianyi oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:422 year:2015 number:2 day:15 month:02 pages:920-939 extent:20 https://doi.org/10.1016/j.jmaa.2014.08.058 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 422 2015 2 15 0215 920-939 20 045F 510 |
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10.1016/j.jmaa.2014.08.058 doi GBVA2015022000019.pica (DE-627)ELV01894518X (ELSEVIER)S0022-247X(14)00810-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 44.40 bkl Wang, Cheng verfasserin aut Further investigations into the stability and bifurcation of a discrete predator–prey model 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. Discrete predator–prey model Elsevier Project Method Elsevier Flip bifurcation Elsevier Fold bifurcation Elsevier Center Manifold Theorem Elsevier Li, Xianyi oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:422 year:2015 number:2 day:15 month:02 pages:920-939 extent:20 https://doi.org/10.1016/j.jmaa.2014.08.058 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 422 2015 2 15 0215 920-939 20 045F 510 |
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10.1016/j.jmaa.2014.08.058 doi GBVA2015022000019.pica (DE-627)ELV01894518X (ELSEVIER)S0022-247X(14)00810-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 610 VZ 44.40 bkl Wang, Cheng verfasserin aut Further investigations into the stability and bifurcation of a discrete predator–prey model 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. Discrete predator–prey model Elsevier Project Method Elsevier Flip bifurcation Elsevier Fold bifurcation Elsevier Center Manifold Theorem Elsevier Li, Xianyi oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:422 year:2015 number:2 day:15 month:02 pages:920-939 extent:20 https://doi.org/10.1016/j.jmaa.2014.08.058 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 422 2015 2 15 0215 920-939 20 045F 510 |
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Enthalten in In silico drug repurposing in COVID-19: A network-based analysis Amsterdam [u.a.] volume:422 year:2015 number:2 day:15 month:02 pages:920-939 extent:20 |
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First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. 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further investigations into the stability and bifurcation of a discrete predator–prey model |
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Further investigations into the stability and bifurcation of a discrete predator–prey model |
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In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. |
| abstractGer |
In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. |
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In this paper we revisit a discrete predator–prey model with a non-monotonic functional response, originally presented in Hu, Teng, and Zhang (2011) [6]. First, by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points E 3 and E 4 obtained in this article, we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria. Here, we present a very useful lemma, which is a corrected version of a known result, and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system. We then study the stability and bifurcation for the equilibrium point E 1 of this system, which has not been considered in any known literature. Unlike known results that present a large number of mathematical formulae that are not easily verified, we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation, which are explicitly expressed by the coefficient of the system. The center manifold theory and Project Method are the main tools in the analysis of bifurcations. The theoretical results obtained are further illustrated by numerical simulations. |
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