A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains

In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Yigit, Gulsemay [verfasserIn] Sarfaraz, Wakil [verfasserIn] Barreira, Raquel [verfasserIn] Madzvamuse, Anotida [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains

Übergeordnetes Werk:	Enthalten in: Nonlinear analysis / Real world applications - Amsterdam [u.a.] : Elsevier Science, 2000, 77
Übergeordnetes Werk:	volume:77

DOI / URN:	10.1016/j.nonrwa.2023.104042

Katalog-ID:	ELV066963109

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100	1		\|a Yigit, Gulsemay \|e verfasserin \|0 (orcid)0000-0003-4442-9151 \|4 aut
245	1	0	\|a A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
264		1	\|c 2023
336			\|a nicht spezifiziert \|b zzz \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development.
650		4	\|a Reaction–cross–diffusion systems
650		4	\|a Domain-dependent instability
650		4	\|a Cross-diffusion-driven instability
650		4	\|a Pattern formation
650		4	\|a Spatiotemporal dynamics
650		4	\|a Circular disc domains
700	1		\|a Sarfaraz, Wakil \|e verfasserin \|4 aut
700	1		\|a Barreira, Raquel \|e verfasserin \|4 aut
700	1		\|a Madzvamuse, Anotida \|e verfasserin \|0 (orcid)0000-0002-9511-8903 \|4 aut
773	0	8	\|i Enthalten in \|t Nonlinear analysis / Real world applications \|d Amsterdam [u.a.] : Elsevier Science, 2000 \|g 77 \|h Online-Ressource \|w (DE-627)336799039 \|w (DE-600)2061967-4 \|w (DE-576)099718286 \|7 nnns
773	1	8	\|g volume:77
912			\|a GBV_USEFLAG_U
912			\|a GBV_ELV
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.55 \|j Globale Analysis \|q VZ
936	b	k	\|a 31.46 \|j Funktionalanalysis \|q VZ
951			\|a AR
952			\|d 77

Indexfelder

author_variant	g y gy w s ws r b rb a m am
matchkey_str	yigitgulsemaysarfarazwakilbarreiraraquel:2023----:dmidpnettbltaayioratodfuinytmwtlnacos
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bklnumber	31.55 31.46
publishDate	2023
allfields	10.1016/j.nonrwa.2023.104042 doi (DE-627)ELV066963109 (ELSEVIER)S1468-1218(23)00212-2 DE-627 ger DE-627 rda eng 510 VZ 31.55 bkl 31.46 bkl Yigit, Gulsemay verfasserin (orcid)0000-0003-4442-9151 aut A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development. Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains Sarfaraz, Wakil verfasserin aut Barreira, Raquel verfasserin aut Madzvamuse, Anotida verfasserin (orcid)0000-0002-9511-8903 aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 77 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:77 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.55 Globale Analysis VZ 31.46 Funktionalanalysis VZ AR 77
spelling	10.1016/j.nonrwa.2023.104042 doi (DE-627)ELV066963109 (ELSEVIER)S1468-1218(23)00212-2 DE-627 ger DE-627 rda eng 510 VZ 31.55 bkl 31.46 bkl Yigit, Gulsemay verfasserin (orcid)0000-0003-4442-9151 aut A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development. Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains Sarfaraz, Wakil verfasserin aut Barreira, Raquel verfasserin aut Madzvamuse, Anotida verfasserin (orcid)0000-0002-9511-8903 aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 77 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:77 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.55 Globale Analysis VZ 31.46 Funktionalanalysis VZ AR 77
allfields_unstemmed	10.1016/j.nonrwa.2023.104042 doi (DE-627)ELV066963109 (ELSEVIER)S1468-1218(23)00212-2 DE-627 ger DE-627 rda eng 510 VZ 31.55 bkl 31.46 bkl Yigit, Gulsemay verfasserin (orcid)0000-0003-4442-9151 aut A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development. Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains Sarfaraz, Wakil verfasserin aut Barreira, Raquel verfasserin aut Madzvamuse, Anotida verfasserin (orcid)0000-0002-9511-8903 aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 77 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:77 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.55 Globale Analysis VZ 31.46 Funktionalanalysis VZ AR 77
allfieldsGer	10.1016/j.nonrwa.2023.104042 doi (DE-627)ELV066963109 (ELSEVIER)S1468-1218(23)00212-2 DE-627 ger DE-627 rda eng 510 VZ 31.55 bkl 31.46 bkl Yigit, Gulsemay verfasserin (orcid)0000-0003-4442-9151 aut A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development. Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains Sarfaraz, Wakil verfasserin aut Barreira, Raquel verfasserin aut Madzvamuse, Anotida verfasserin (orcid)0000-0002-9511-8903 aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 77 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:77 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.55 Globale Analysis VZ 31.46 Funktionalanalysis VZ AR 77
allfieldsSound	10.1016/j.nonrwa.2023.104042 doi (DE-627)ELV066963109 (ELSEVIER)S1468-1218(23)00212-2 DE-627 ger DE-627 rda eng 510 VZ 31.55 bkl 31.46 bkl Yigit, Gulsemay verfasserin (orcid)0000-0003-4442-9151 aut A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development. Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains Sarfaraz, Wakil verfasserin aut Barreira, Raquel verfasserin aut Madzvamuse, Anotida verfasserin (orcid)0000-0002-9511-8903 aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 77 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:77 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.55 Globale Analysis VZ 31.46 Funktionalanalysis VZ AR 77
language	English
source	Enthalten in Nonlinear analysis / Real world applications 77 volume:77
sourceStr	Enthalten in Nonlinear analysis / Real world applications 77 volume:77
format_phy_str_mv	Article
bklname	Globale Analysis Funktionalanalysis
institution	findex.gbv.de
topic_facet	Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains
dewey-raw	510
isfreeaccess_bool	false
container_title	Nonlinear analysis / Real world applications
authorswithroles_txt_mv	Yigit, Gulsemay @@aut@@ Sarfaraz, Wakil @@aut@@ Barreira, Raquel @@aut@@ Madzvamuse, Anotida @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	336799039
dewey-sort	3510
id	ELV066963109
language_de	englisch
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The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. 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author	Yigit, Gulsemay
spellingShingle	Yigit, Gulsemay ddc 510 bkl 31.55 bkl 31.46 misc Reaction–cross–diffusion systems misc Domain-dependent instability misc Cross-diffusion-driven instability misc Pattern formation misc Spatiotemporal dynamics misc Circular disc domains A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
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topic_title	510 VZ 31.55 bkl 31.46 bkl A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains Reaction–cross–diffusion systems Domain-dependent instability Cross-diffusion-driven instability Pattern formation Spatiotemporal dynamics Circular disc domains
topic	ddc 510 bkl 31.55 bkl 31.46 misc Reaction–cross–diffusion systems misc Domain-dependent instability misc Cross-diffusion-driven instability misc Pattern formation misc Spatiotemporal dynamics misc Circular disc domains
topic_unstemmed	ddc 510 bkl 31.55 bkl 31.46 misc Reaction–cross–diffusion systems misc Domain-dependent instability misc Cross-diffusion-driven instability misc Pattern formation misc Spatiotemporal dynamics misc Circular disc domains
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title	A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
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title_full	A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
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title_sort	a domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
title_auth	A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
abstract	In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development.
abstractGer	In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development.
abstract_unstemmed	In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development.
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title_short	A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
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The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reaction–cross–diffusion systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Domain-dependent instability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cross-diffusion-driven instability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pattern formation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spatiotemporal dynamics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Circular disc domains</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sarfaraz, Wakil</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Barreira, Raquel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Madzvamuse, Anotida</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-9511-8903</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Nonlinear analysis / Real world applications</subfield><subfield code="d">Amsterdam [u.a.] : Elsevier Science, 2000</subfield><subfield code="g">77</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)336799039</subfield><subfield code="w">(DE-600)2061967-4</subfield><subfield code="w">(DE-576)099718286</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:77</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield 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A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains

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