Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System

In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation t...
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Autor*in:	Meng Lin [verfasserIn] Yanyou Chai [verfasserIn] Xuguang Yang [verfasserIn] Yufeng Wang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Übergeordnetes Werk:	In: Mathematical Problems in Engineering - Hindawi Limited, 2002, (2019)
Übergeordnetes Werk:	year:2019

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.1155/2019/3907453

Katalog-ID:	DOAJ066753430

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spelling	10.1155/2019/3907453 doi (DE-627)DOAJ066753430 (DE-599)DOAJ7e5336699e0d4b41b4238332cf2b1163 DE-627 ger DE-627 rakwb eng TA1-2040 QA1-939 Meng Lin verfasserin aut Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology. Engineering (General). Civil engineering (General) Mathematics Yanyou Chai verfasserin aut Xuguang Yang verfasserin aut Yufeng Wang verfasserin aut In Mathematical Problems in Engineering Hindawi Limited, 2002 (2019) (DE-627)320519937 (DE-600)2014442-8 1024123X nnns year:2019 https://doi.org/10.1155/2019/3907453 kostenfrei https://doaj.org/article/7e5336699e0d4b41b4238332cf2b1163 kostenfrei http://dx.doi.org/10.1155/2019/3907453 kostenfrei https://doaj.org/toc/1024-123X Journal toc kostenfrei https://doaj.org/toc/1563-5147 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2336 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 AR 2019
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allfieldsSound	10.1155/2019/3907453 doi (DE-627)DOAJ066753430 (DE-599)DOAJ7e5336699e0d4b41b4238332cf2b1163 DE-627 ger DE-627 rakwb eng TA1-2040 QA1-939 Meng Lin verfasserin aut Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology. Engineering (General). Civil engineering (General) Mathematics Yanyou Chai verfasserin aut Xuguang Yang verfasserin aut Yufeng Wang verfasserin aut In Mathematical Problems in Engineering Hindawi Limited, 2002 (2019) (DE-627)320519937 (DE-600)2014442-8 1024123X nnns year:2019 https://doi.org/10.1155/2019/3907453 kostenfrei https://doaj.org/article/7e5336699e0d4b41b4238332cf2b1163 kostenfrei http://dx.doi.org/10.1155/2019/3907453 kostenfrei https://doaj.org/toc/1024-123X Journal toc kostenfrei https://doaj.org/toc/1563-5147 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2336 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 AR 2019
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title	Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System
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title_sort	spatiotemporal patterns induced by hopf bifurcations in a homogeneous diffusive predator-prey system
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title_auth	Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System
abstract	In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology.
abstractGer	In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology.
abstract_unstemmed	In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology.
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title_short	Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator-Prey System
url	https://doi.org/10.1155/2019/3907453 https://doaj.org/article/7e5336699e0d4b41b4238332cf2b1163 http://dx.doi.org/10.1155/2019/3907453 https://doaj.org/toc/1024-123X https://doaj.org/toc/1563-5147
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