Generalized flip and strong resonances bifurcations of a predator–prey model

Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codim...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Eskandari, Zohreh [verfasserIn] Alidousti, Javad [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Bifurcation Stability Predator–prey model Neimark–Sacker Fold Flip Strong resonance Generalized flip Allee effect

Übergeordnetes Werk:	Enthalten in: International journal of dynamics and control - Berlin : Springer, 2013, 9(2020), 1 vom: 19. Mai, Seite 275-287
Übergeordnetes Werk:	volume:9 ; year:2020 ; number:1 ; day:19 ; month:05 ; pages:275-287

Links:	Volltext

DOI / URN:	10.1007/s40435-020-00637-8

Katalog-ID:	SPR04308950X

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245	1	0	\|a Generalized flip and strong resonances bifurcations of a predator–prey model
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520			\|a Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model.
650		4	\|a Bifurcation \|7 (dpeaa)DE-He213
650		4	\|a Stability \|7 (dpeaa)DE-He213
650		4	\|a Predator–prey model \|7 (dpeaa)DE-He213
650		4	\|a Neimark–Sacker \|7 (dpeaa)DE-He213
650		4	\|a Fold \|7 (dpeaa)DE-He213
650		4	\|a Flip \|7 (dpeaa)DE-He213
650		4	\|a Strong resonance \|7 (dpeaa)DE-He213
650		4	\|a Generalized flip \|7 (dpeaa)DE-He213
650		4	\|a Allee effect \|7 (dpeaa)DE-He213
700	1		\|a Alidousti, Javad \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t International journal of dynamics and control \|d Berlin : Springer, 2013 \|g 9(2020), 1 vom: 19. Mai, Seite 275-287 \|w (DE-627)745617794 \|w (DE-600)2714518-9 \|x 2195-2698 \|7 nnns
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allfields	10.1007/s40435-020-00637-8 doi (DE-627)SPR04308950X (DE-599)SPRs40435-020-00637-8-e (SPR)s40435-020-00637-8-e DE-627 ger DE-627 rakwb eng 510 ASE Eskandari, Zohreh verfasserin aut Generalized flip and strong resonances bifurcations of a predator–prey model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model. Bifurcation (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Predator–prey model (dpeaa)DE-He213 Neimark–Sacker (dpeaa)DE-He213 Fold (dpeaa)DE-He213 Flip (dpeaa)DE-He213 Strong resonance (dpeaa)DE-He213 Generalized flip (dpeaa)DE-He213 Allee effect (dpeaa)DE-He213 Alidousti, Javad verfasserin aut Enthalten in International journal of dynamics and control Berlin : Springer, 2013 9(2020), 1 vom: 19. Mai, Seite 275-287 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:9 year:2020 number:1 day:19 month:05 pages:275-287 https://dx.doi.org/10.1007/s40435-020-00637-8 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_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_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_4277 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 9 2020 1 19 05 275-287
spelling	10.1007/s40435-020-00637-8 doi (DE-627)SPR04308950X (DE-599)SPRs40435-020-00637-8-e (SPR)s40435-020-00637-8-e DE-627 ger DE-627 rakwb eng 510 ASE Eskandari, Zohreh verfasserin aut Generalized flip and strong resonances bifurcations of a predator–prey model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model. Bifurcation (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Predator–prey model (dpeaa)DE-He213 Neimark–Sacker (dpeaa)DE-He213 Fold (dpeaa)DE-He213 Flip (dpeaa)DE-He213 Strong resonance (dpeaa)DE-He213 Generalized flip (dpeaa)DE-He213 Allee effect (dpeaa)DE-He213 Alidousti, Javad verfasserin aut Enthalten in International journal of dynamics and control Berlin : Springer, 2013 9(2020), 1 vom: 19. Mai, Seite 275-287 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:9 year:2020 number:1 day:19 month:05 pages:275-287 https://dx.doi.org/10.1007/s40435-020-00637-8 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_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_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_4277 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 9 2020 1 19 05 275-287
allfields_unstemmed	10.1007/s40435-020-00637-8 doi (DE-627)SPR04308950X (DE-599)SPRs40435-020-00637-8-e (SPR)s40435-020-00637-8-e DE-627 ger DE-627 rakwb eng 510 ASE Eskandari, Zohreh verfasserin aut Generalized flip and strong resonances bifurcations of a predator–prey model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model. Bifurcation (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Predator–prey model (dpeaa)DE-He213 Neimark–Sacker (dpeaa)DE-He213 Fold (dpeaa)DE-He213 Flip (dpeaa)DE-He213 Strong resonance (dpeaa)DE-He213 Generalized flip (dpeaa)DE-He213 Allee effect (dpeaa)DE-He213 Alidousti, Javad verfasserin aut Enthalten in International journal of dynamics and control Berlin : Springer, 2013 9(2020), 1 vom: 19. Mai, Seite 275-287 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:9 year:2020 number:1 day:19 month:05 pages:275-287 https://dx.doi.org/10.1007/s40435-020-00637-8 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_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_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_4277 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 9 2020 1 19 05 275-287
allfieldsGer	10.1007/s40435-020-00637-8 doi (DE-627)SPR04308950X (DE-599)SPRs40435-020-00637-8-e (SPR)s40435-020-00637-8-e DE-627 ger DE-627 rakwb eng 510 ASE Eskandari, Zohreh verfasserin aut Generalized flip and strong resonances bifurcations of a predator–prey model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model. Bifurcation (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Predator–prey model (dpeaa)DE-He213 Neimark–Sacker (dpeaa)DE-He213 Fold (dpeaa)DE-He213 Flip (dpeaa)DE-He213 Strong resonance (dpeaa)DE-He213 Generalized flip (dpeaa)DE-He213 Allee effect (dpeaa)DE-He213 Alidousti, Javad verfasserin aut Enthalten in International journal of dynamics and control Berlin : Springer, 2013 9(2020), 1 vom: 19. Mai, Seite 275-287 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:9 year:2020 number:1 day:19 month:05 pages:275-287 https://dx.doi.org/10.1007/s40435-020-00637-8 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_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_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_4277 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 9 2020 1 19 05 275-287
allfieldsSound	10.1007/s40435-020-00637-8 doi (DE-627)SPR04308950X (DE-599)SPRs40435-020-00637-8-e (SPR)s40435-020-00637-8-e DE-627 ger DE-627 rakwb eng 510 ASE Eskandari, Zohreh verfasserin aut Generalized flip and strong resonances bifurcations of a predator–prey model 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model. Bifurcation (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Predator–prey model (dpeaa)DE-He213 Neimark–Sacker (dpeaa)DE-He213 Fold (dpeaa)DE-He213 Flip (dpeaa)DE-He213 Strong resonance (dpeaa)DE-He213 Generalized flip (dpeaa)DE-He213 Allee effect (dpeaa)DE-He213 Alidousti, Javad verfasserin aut Enthalten in International journal of dynamics and control Berlin : Springer, 2013 9(2020), 1 vom: 19. Mai, Seite 275-287 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:9 year:2020 number:1 day:19 month:05 pages:275-287 https://dx.doi.org/10.1007/s40435-020-00637-8 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_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_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_4277 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 9 2020 1 19 05 275-287
language	English
source	Enthalten in International journal of dynamics and control 9(2020), 1 vom: 19. Mai, Seite 275-287 volume:9 year:2020 number:1 day:19 month:05 pages:275-287
sourceStr	Enthalten in International journal of dynamics and control 9(2020), 1 vom: 19. Mai, Seite 275-287 volume:9 year:2020 number:1 day:19 month:05 pages:275-287
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Bifurcation Stability Predator–prey model Neimark–Sacker Fold Flip Strong resonance Generalized flip Allee effect
dewey-raw	510
isfreeaccess_bool	false
container_title	International journal of dynamics and control
authorswithroles_txt_mv	Eskandari, Zohreh @@aut@@ Alidousti, Javad @@aut@@
publishDateDaySort_date	2020-05-19T00:00:00Z
hierarchy_top_id	745617794
dewey-sort	3510
id	SPR04308950X
language_de	englisch
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Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. 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author	Eskandari, Zohreh
spellingShingle	Eskandari, Zohreh ddc 510 misc Bifurcation misc Stability misc Predator–prey model misc Neimark–Sacker misc Fold misc Flip misc Strong resonance misc Generalized flip misc Allee effect Generalized flip and strong resonances bifurcations of a predator–prey model
authorStr	Eskandari, Zohreh
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topic_title	510 ASE Generalized flip and strong resonances bifurcations of a predator–prey model Bifurcation (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Predator–prey model (dpeaa)DE-He213 Neimark–Sacker (dpeaa)DE-He213 Fold (dpeaa)DE-He213 Flip (dpeaa)DE-He213 Strong resonance (dpeaa)DE-He213 Generalized flip (dpeaa)DE-He213 Allee effect (dpeaa)DE-He213
topic	ddc 510 misc Bifurcation misc Stability misc Predator–prey model misc Neimark–Sacker misc Fold misc Flip misc Strong resonance misc Generalized flip misc Allee effect
topic_unstemmed	ddc 510 misc Bifurcation misc Stability misc Predator–prey model misc Neimark–Sacker misc Fold misc Flip misc Strong resonance misc Generalized flip misc Allee effect
topic_browse	ddc 510 misc Bifurcation misc Stability misc Predator–prey model misc Neimark–Sacker misc Fold misc Flip misc Strong resonance misc Generalized flip misc Allee effect
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Generalized flip and strong resonances bifurcations of a predator–prey model
ctrlnum	(DE-627)SPR04308950X (DE-599)SPRs40435-020-00637-8-e (SPR)s40435-020-00637-8-e
title_full	Generalized flip and strong resonances bifurcations of a predator–prey model
author_sort	Eskandari, Zohreh
journal	International journal of dynamics and control
journalStr	International journal of dynamics and control
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author_browse	Eskandari, Zohreh Alidousti, Javad
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author-letter	Eskandari, Zohreh
doi_str_mv	10.1007/s40435-020-00637-8
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title_sort	generalized flip and strong resonances bifurcations of a predator–prey model
title_auth	Generalized flip and strong resonances bifurcations of a predator–prey model
abstract	Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model.
abstractGer	Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model.
abstract_unstemmed	Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model.
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title_short	Generalized flip and strong resonances bifurcations of a predator–prey model
url	https://dx.doi.org/10.1007/s40435-020-00637-8
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author2	Alidousti, Javad
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doi_str	10.1007/s40435-020-00637-8
up_date	2024-07-03T16:33:37.781Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR04308950X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220112023737.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">210209s2020 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40435-020-00637-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR04308950X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)SPRs40435-020-00637-8-e</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40435-020-00637-8-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Eskandari, Zohreh</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Generalized flip and strong resonances bifurcations of a predator–prey model</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, bifurcation analysis of a predator–prey discrete model equipped with Allee effect has been carried out both analytically and numerically. Stability circumstances of three fixed points of this model is represented briefly. In this study is shown that this model undergoes codimension one (codim-1) bifurcations such as the transcritical, fold, flip and Neimark–Sacker. Besides, codimension two (codim-2) bifurcations including the generalized flip, resonances 1:2, 1:3, 1:4 have been achieved. The non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore the computing the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations are needed. Using the critical normal form coefficients method to examine the bifurcation analysis makes it to avoid calculating the central manifold and converting the linear part of the map into Jordan form. This is one of the most effective methods in the bifurcation analysis that has not received much attention so far. So in this article our attention are turned to this method. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. The bifurcation curves of fixed points under variation of one and two parameters and all codim-1,2 bifurcations curves are computed by using numerical methods in the numerical software matcontm. In the following, our represented analysis is proved by numerical simulation and displays more complex behaviours of model.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bifurcation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Predator–prey model</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Neimark–Sacker</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fold</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Flip</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong resonance</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Generalized flip</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Allee effect</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Alidousti, Javad</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">International journal of dynamics and control</subfield><subfield code="d">Berlin : Springer, 2013</subfield><subfield code="g">9(2020), 1 vom: 19. Mai, Seite 275-287</subfield><subfield code="w">(DE-627)745617794</subfield><subfield code="w">(DE-600)2714518-9</subfield><subfield code="x">2195-2698</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:9</subfield><subfield code="g">year:2020</subfield><subfield code="g">number:1</subfield><subfield code="g">day:19</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:275-287</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s40435-020-00637-8</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" 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Generalized flip and strong resonances bifurcations of a predator–prey model

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