A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey
Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive dif...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Li, Shunyi [verfasserIn] Liu, Wenwu [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Advances in difference equations - [S.l.] : Springer International, 2004, 2016(2016), 1 vom: 05. Feb. |
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| Übergeordnetes Werk: |
volume:2016 ; year:2016 ; number:1 ; day:05 ; month:02 |
| Links: |
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| DOI / URN: |
10.1186/s13662-016-0768-8 |
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| Katalog-ID: |
SPR032098928 |
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| 520 | |a Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. | ||
| 650 | 4 | |a predator-prey system |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a impulsive perturbation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a time delay |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a extinction |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a permanence |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a chaos |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Liu, Wenwu |e verfasserin |4 aut | |
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10.1186/s13662-016-0768-8 doi (DE-627)SPR032098928 (SPR)s13662-016-0768-8-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Li, Shunyi verfasserin aut A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. predator-prey system (dpeaa)DE-He213 impulsive perturbation (dpeaa)DE-He213 time delay (dpeaa)DE-He213 extinction (dpeaa)DE-He213 permanence (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Liu, Wenwu verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2016(2016), 1 vom: 05. Feb. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2016 year:2016 number:1 day:05 month:02 https://dx.doi.org/10.1186/s13662-016-0768-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2016 2016 1 05 02 |
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10.1186/s13662-016-0768-8 doi (DE-627)SPR032098928 (SPR)s13662-016-0768-8-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Li, Shunyi verfasserin aut A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. predator-prey system (dpeaa)DE-He213 impulsive perturbation (dpeaa)DE-He213 time delay (dpeaa)DE-He213 extinction (dpeaa)DE-He213 permanence (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Liu, Wenwu verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2016(2016), 1 vom: 05. Feb. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2016 year:2016 number:1 day:05 month:02 https://dx.doi.org/10.1186/s13662-016-0768-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2016 2016 1 05 02 |
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10.1186/s13662-016-0768-8 doi (DE-627)SPR032098928 (SPR)s13662-016-0768-8-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Li, Shunyi verfasserin aut A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. predator-prey system (dpeaa)DE-He213 impulsive perturbation (dpeaa)DE-He213 time delay (dpeaa)DE-He213 extinction (dpeaa)DE-He213 permanence (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Liu, Wenwu verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2016(2016), 1 vom: 05. Feb. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2016 year:2016 number:1 day:05 month:02 https://dx.doi.org/10.1186/s13662-016-0768-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2016 2016 1 05 02 |
| allfieldsGer |
10.1186/s13662-016-0768-8 doi (DE-627)SPR032098928 (SPR)s13662-016-0768-8-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Li, Shunyi verfasserin aut A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. predator-prey system (dpeaa)DE-He213 impulsive perturbation (dpeaa)DE-He213 time delay (dpeaa)DE-He213 extinction (dpeaa)DE-He213 permanence (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Liu, Wenwu verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2016(2016), 1 vom: 05. Feb. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2016 year:2016 number:1 day:05 month:02 https://dx.doi.org/10.1186/s13662-016-0768-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2016 2016 1 05 02 |
| allfieldsSound |
10.1186/s13662-016-0768-8 doi (DE-627)SPR032098928 (SPR)s13662-016-0768-8-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Li, Shunyi verfasserin aut A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. predator-prey system (dpeaa)DE-He213 impulsive perturbation (dpeaa)DE-He213 time delay (dpeaa)DE-He213 extinction (dpeaa)DE-He213 permanence (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Liu, Wenwu verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2016(2016), 1 vom: 05. Feb. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2016 year:2016 number:1 day:05 month:02 https://dx.doi.org/10.1186/s13662-016-0768-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2016 2016 1 05 02 |
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Li, Shunyi |
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Li, Shunyi ddc 510 bkl 31.49 misc predator-prey system misc impulsive perturbation misc time delay misc extinction misc permanence misc chaos A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey |
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delayed holling type iii functional response predator-prey system with impulsive perturbation on the prey |
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A delayed Holling type III functional response predator-prey system with impulsive perturbation on the prey |
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Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. |
| abstractGer |
Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. |
| abstract_unstemmed |
Abstract A Holling type III functional response predator-prey system with constant gestation time delay and impulsive perturbation on the prey is investigated. The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. Finally, the impulsive control strategy and the biological implications of the results are discussed. |
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The sufficient conditions for the global attractivity of a predator-extinction periodic solution are obtained by the theory of impulsive differential equations, i.e. the impulsive period is less than the critical value $T_{1}^{*}$. The conditions for the permanence of the system are investigated, i.e. the impulsive period is larger than the critical value $T_{2}^{*}$. Numerical examples show that the system has very complex dynamic behaviors, including (1) high-order periodic and quasi-periodic oscillations, (2) period-doubling and -halving bifurcations, and (3) chaos and attractor crises. Further, the importance of the impulsive period, the gestation time delay, and the impulsive perturbation proportionality constant are discussed. 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