Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model
Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator w...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dong, Yuxin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Zeitschrift für angewandte Mathematik und Physik - Cham (ZG) : Springer International Publishing AG, 1950, 73(2021), 1 vom: 16. Dez. |
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| Übergeordnetes Werk: |
volume:73 ; year:2021 ; number:1 ; day:16 ; month:12 |
| Links: |
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| DOI / URN: |
10.1007/s00033-021-01659-8 |
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| Katalog-ID: |
SPR045806012 |
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| 100 | 1 | |a Dong, Yuxin |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model |
| 264 | 1 | |c 2021 | |
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| 520 | |a Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. | ||
| 650 | 4 | |a Predator-taxis sensitivity |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Fear effect |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Predator–prey |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Hopf bifurcation |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Wu, Daiyong |0 (orcid)0000-0003-4316-7225 |4 aut | |
| 700 | 1 | |a Shen, Chuansheng |4 aut | |
| 700 | 1 | |a Ye, Luhong |4 aut | |
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10.1007/s00033-021-01659-8 doi (DE-627)SPR045806012 (SPR)s00033-021-01659-8-e DE-627 ger DE-627 rakwb eng Dong, Yuxin verfasserin aut Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. Predator-taxis sensitivity (dpeaa)DE-He213 Fear effect (dpeaa)DE-He213 Predator–prey (dpeaa)DE-He213 Hopf bifurcation (dpeaa)DE-He213 Wu, Daiyong (orcid)0000-0003-4316-7225 aut Shen, Chuansheng aut Ye, Luhong aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 73(2021), 1 vom: 16. Dez. (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:73 year:2021 number:1 day:16 month:12 https://dx.doi.org/10.1007/s00033-021-01659-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2021 1 16 12 |
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10.1007/s00033-021-01659-8 doi (DE-627)SPR045806012 (SPR)s00033-021-01659-8-e DE-627 ger DE-627 rakwb eng Dong, Yuxin verfasserin aut Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. Predator-taxis sensitivity (dpeaa)DE-He213 Fear effect (dpeaa)DE-He213 Predator–prey (dpeaa)DE-He213 Hopf bifurcation (dpeaa)DE-He213 Wu, Daiyong (orcid)0000-0003-4316-7225 aut Shen, Chuansheng aut Ye, Luhong aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 73(2021), 1 vom: 16. Dez. (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:73 year:2021 number:1 day:16 month:12 https://dx.doi.org/10.1007/s00033-021-01659-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2021 1 16 12 |
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10.1007/s00033-021-01659-8 doi (DE-627)SPR045806012 (SPR)s00033-021-01659-8-e DE-627 ger DE-627 rakwb eng Dong, Yuxin verfasserin aut Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. Predator-taxis sensitivity (dpeaa)DE-He213 Fear effect (dpeaa)DE-He213 Predator–prey (dpeaa)DE-He213 Hopf bifurcation (dpeaa)DE-He213 Wu, Daiyong (orcid)0000-0003-4316-7225 aut Shen, Chuansheng aut Ye, Luhong aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 73(2021), 1 vom: 16. Dez. (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:73 year:2021 number:1 day:16 month:12 https://dx.doi.org/10.1007/s00033-021-01659-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2021 1 16 12 |
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10.1007/s00033-021-01659-8 doi (DE-627)SPR045806012 (SPR)s00033-021-01659-8-e DE-627 ger DE-627 rakwb eng Dong, Yuxin verfasserin aut Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. Predator-taxis sensitivity (dpeaa)DE-He213 Fear effect (dpeaa)DE-He213 Predator–prey (dpeaa)DE-He213 Hopf bifurcation (dpeaa)DE-He213 Wu, Daiyong (orcid)0000-0003-4316-7225 aut Shen, Chuansheng aut Ye, Luhong aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 73(2021), 1 vom: 16. Dez. (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:73 year:2021 number:1 day:16 month:12 https://dx.doi.org/10.1007/s00033-021-01659-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2021 1 16 12 |
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10.1007/s00033-021-01659-8 doi (DE-627)SPR045806012 (SPR)s00033-021-01659-8-e DE-627 ger DE-627 rakwb eng Dong, Yuxin verfasserin aut Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. Predator-taxis sensitivity (dpeaa)DE-He213 Fear effect (dpeaa)DE-He213 Predator–prey (dpeaa)DE-He213 Hopf bifurcation (dpeaa)DE-He213 Wu, Daiyong (orcid)0000-0003-4316-7225 aut Shen, Chuansheng aut Ye, Luhong aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 73(2021), 1 vom: 16. Dez. (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:73 year:2021 number:1 day:16 month:12 https://dx.doi.org/10.1007/s00033-021-01659-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2021 1 16 12 |
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Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. 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Dong, Yuxin |
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Dong, Yuxin misc Predator-taxis sensitivity misc Fear effect misc Predator–prey misc Hopf bifurcation Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model |
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Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model Predator-taxis sensitivity (dpeaa)DE-He213 Fear effect (dpeaa)DE-He213 Predator–prey (dpeaa)DE-He213 Hopf bifurcation (dpeaa)DE-He213 |
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Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model |
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influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model |
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Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model |
| abstract |
Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
| abstractGer |
Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
| abstract_unstemmed |
Abstract Experiments show that the fear of predators reduces the birth rate of the prey population, but it does not cause the extinction of the prey population. Even if the fear is sufficiently large, the prey can survive under the saturated fear cost. Moreover, the sensitivity of prey to predator will affect the population density of prey and predator. It is feasible to introduce the saturated fear cost and predator-taxis sensitivity into the predator–prey interactions model. In this paper, we obtain the threshold condition of the persistence for the proposed model and discuss all ecologically feasible equilibrium points and their stability in terms of the model parameters. Furthermore, when choose the fear level as bifurcation parameter, the model will arise single Hopf bifurcation point. However, when choose the predator-taxis sensitivity as bifurcation parameter, the model will arise two Hopf bifurcation points. In order to determine the stability of the limit cycle caused by Hopf bifurcation, the first Lyapunov number is calculated in detail. In addition, by the sensitivity analysis and the elasticity analysis, the saturated fear cost takes on the strong impact on the sensitivity for the model, and the predator death rate has a greater impact on the persistence of the model than the prey death rate. Our numerical illustration also shows that the predator-taxis sensitivity determines the success or failure of the predator invasion under appropriate fear level. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 |
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Influence of fear effect and predator-taxis sensitivity on dynamical behavior of a predator–prey model |
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https://dx.doi.org/10.1007/s00033-021-01659-8 |
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Wu, Daiyong Shen, Chuansheng Ye, Luhong |
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Wu, Daiyong Shen, Chuansheng Ye, Luhong |
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10.1007/s00033-021-01659-8 |
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2024-07-03T18:24:43.025Z |
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| score |
7.3985558 |