Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System

Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new sys...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Li, Xianyi [verfasserIn] Liu, Yuqing

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Discrete predator-prey system Ratio-dependent functional response Transcritical bifurcation Period-doubling bifurcation Fold-flip bifurcation

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Qualitative theory of dynamical systems - Basel : Birkhäuser, 1999, 21(2022), 4 vom: 13. Sept.
Übergeordnetes Werk:	volume:21 ; year:2022 ; number:4 ; day:13 ; month:09

Links:	Volltext

DOI / URN:	10.1007/s12346-022-00646-2

Katalog-ID:	SPR048090530

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520			\|a Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations.
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650		4	\|a Transcritical bifurcation \|7 (dpeaa)DE-He213
650		4	\|a Period-doubling bifurcation \|7 (dpeaa)DE-He213
650		4	\|a Fold-flip bifurcation \|7 (dpeaa)DE-He213
700	1		\|a Liu, Yuqing \|4 aut
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912			\|a GBV_ILN_187
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author_variant	x l xl y l yl
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allfields	10.1007/s12346-022-00646-2 doi (DE-627)SPR048090530 (SPR)s12346-022-00646-2-e DE-627 ger DE-627 rakwb eng Li, Xianyi verfasserin aut Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. Discrete predator-prey system (dpeaa)DE-He213 Ratio-dependent functional response (dpeaa)DE-He213 Transcritical bifurcation (dpeaa)DE-He213 Period-doubling bifurcation (dpeaa)DE-He213 Fold-flip bifurcation (dpeaa)DE-He213 Liu, Yuqing aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 4 vom: 13. Sept. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:4 day:13 month:09 https://dx.doi.org/10.1007/s12346-022-00646-2 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_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 21 2022 4 13 09
spelling	10.1007/s12346-022-00646-2 doi (DE-627)SPR048090530 (SPR)s12346-022-00646-2-e DE-627 ger DE-627 rakwb eng Li, Xianyi verfasserin aut Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. Discrete predator-prey system (dpeaa)DE-He213 Ratio-dependent functional response (dpeaa)DE-He213 Transcritical bifurcation (dpeaa)DE-He213 Period-doubling bifurcation (dpeaa)DE-He213 Fold-flip bifurcation (dpeaa)DE-He213 Liu, Yuqing aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 4 vom: 13. Sept. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:4 day:13 month:09 https://dx.doi.org/10.1007/s12346-022-00646-2 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_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 21 2022 4 13 09
allfields_unstemmed	10.1007/s12346-022-00646-2 doi (DE-627)SPR048090530 (SPR)s12346-022-00646-2-e DE-627 ger DE-627 rakwb eng Li, Xianyi verfasserin aut Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. Discrete predator-prey system (dpeaa)DE-He213 Ratio-dependent functional response (dpeaa)DE-He213 Transcritical bifurcation (dpeaa)DE-He213 Period-doubling bifurcation (dpeaa)DE-He213 Fold-flip bifurcation (dpeaa)DE-He213 Liu, Yuqing aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 4 vom: 13. Sept. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:4 day:13 month:09 https://dx.doi.org/10.1007/s12346-022-00646-2 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_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 21 2022 4 13 09
allfieldsGer	10.1007/s12346-022-00646-2 doi (DE-627)SPR048090530 (SPR)s12346-022-00646-2-e DE-627 ger DE-627 rakwb eng Li, Xianyi verfasserin aut Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. Discrete predator-prey system (dpeaa)DE-He213 Ratio-dependent functional response (dpeaa)DE-He213 Transcritical bifurcation (dpeaa)DE-He213 Period-doubling bifurcation (dpeaa)DE-He213 Fold-flip bifurcation (dpeaa)DE-He213 Liu, Yuqing aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 4 vom: 13. Sept. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:4 day:13 month:09 https://dx.doi.org/10.1007/s12346-022-00646-2 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_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 21 2022 4 13 09
allfieldsSound	10.1007/s12346-022-00646-2 doi (DE-627)SPR048090530 (SPR)s12346-022-00646-2-e DE-627 ger DE-627 rakwb eng Li, Xianyi verfasserin aut Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. Discrete predator-prey system (dpeaa)DE-He213 Ratio-dependent functional response (dpeaa)DE-He213 Transcritical bifurcation (dpeaa)DE-He213 Period-doubling bifurcation (dpeaa)DE-He213 Fold-flip bifurcation (dpeaa)DE-He213 Liu, Yuqing aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 4 vom: 13. Sept. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:4 day:13 month:09 https://dx.doi.org/10.1007/s12346-022-00646-2 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_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 21 2022 4 13 09
language	English
source	Enthalten in Qualitative theory of dynamical systems 21(2022), 4 vom: 13. Sept. volume:21 year:2022 number:4 day:13 month:09
sourceStr	Enthalten in Qualitative theory of dynamical systems 21(2022), 4 vom: 13. Sept. volume:21 year:2022 number:4 day:13 month:09
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Discrete predator-prey system Ratio-dependent functional response Transcritical bifurcation Period-doubling bifurcation Fold-flip bifurcation
isfreeaccess_bool	false
container_title	Qualitative theory of dynamical systems
authorswithroles_txt_mv	Li, Xianyi @@aut@@ Liu, Yuqing @@aut@@
publishDateDaySort_date	2022-09-13T00:00:00Z
hierarchy_top_id	582026512
id	SPR048090530
language_de	englisch
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Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. 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author	Li, Xianyi
spellingShingle	Li, Xianyi misc Discrete predator-prey system misc Ratio-dependent functional response misc Transcritical bifurcation misc Period-doubling bifurcation misc Fold-flip bifurcation Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System
authorStr	Li, Xianyi
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topic_title	Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System Discrete predator-prey system (dpeaa)DE-He213 Ratio-dependent functional response (dpeaa)DE-He213 Transcritical bifurcation (dpeaa)DE-He213 Period-doubling bifurcation (dpeaa)DE-He213 Fold-flip bifurcation (dpeaa)DE-He213
topic	misc Discrete predator-prey system misc Ratio-dependent functional response misc Transcritical bifurcation misc Period-doubling bifurcation misc Fold-flip bifurcation
topic_unstemmed	misc Discrete predator-prey system misc Ratio-dependent functional response misc Transcritical bifurcation misc Period-doubling bifurcation misc Fold-flip bifurcation
topic_browse	misc Discrete predator-prey system misc Ratio-dependent functional response misc Transcritical bifurcation misc Period-doubling bifurcation misc Fold-flip bifurcation
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title	Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System
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title_full	Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System
author_sort	Li, Xianyi
journal	Qualitative theory of dynamical systems
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author_browse	Li, Xianyi Liu, Yuqing
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doi_str_mv	10.1007/s12346-022-00646-2
title_sort	transcritical bifurcation and flip bifurcation of a new discrete ratio-dependent predator-prey system
title_auth	Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System
abstract	Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium %$E_3%$ have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria %$E_1%$, %$E_2%$ and %$E_3%$ to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics—chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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container_issue	4
title_short	Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System
url	https://dx.doi.org/10.1007/s12346-022-00646-2
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author2	Liu, Yuqing
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doi_str	10.1007/s12346-022-00646-2
up_date	2024-07-03T16:56:27.916Z
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Transcritical Bifurcation and Flip Bifurcation of a New Discrete Ratio-Dependent Predator-Prey System

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