Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion
Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders...
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Gespeichert in:
| Autor*in: |
Datsko, B. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Nature Switzerland AG 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical chemistry - Springer International Publishing, 1987, 58(2019), 3 vom: 26. Nov., Seite 612-631 |
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| Übergeordnetes Werk: |
volume:58 ; year:2019 ; number:3 ; day:26 ; month:11 ; pages:612-631 |
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| DOI / URN: |
10.1007/s10910-019-01089-y |
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OLC2060427037 |
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| 520 | |a Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented. | ||
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10.1007/s10910-019-01089-y doi (DE-627)OLC2060427037 (DE-He213)s10910-019-01089-y-p DE-627 ger DE-627 rakwb eng 510 540 VZ Datsko, B. verfasserin (orcid)0000-0002-9700-669X aut Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature Switzerland AG 2019 Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented. Mathematical modeling Autocatalytic chemical reaction Self-organization phenomena Anomalous diffusion Reaction–diffusion systems Kutniv, M. aut Włoch, A. aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 58(2019), 3 vom: 26. Nov., Seite 612-631 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:58 year:2019 number:3 day:26 month:11 pages:612-631 https://doi.org/10.1007/s10910-019-01089-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 AR 58 2019 3 26 11 612-631 |
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10.1007/s10910-019-01089-y doi (DE-627)OLC2060427037 (DE-He213)s10910-019-01089-y-p DE-627 ger DE-627 rakwb eng 510 540 VZ Datsko, B. verfasserin (orcid)0000-0002-9700-669X aut Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature Switzerland AG 2019 Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented. Mathematical modeling Autocatalytic chemical reaction Self-organization phenomena Anomalous diffusion Reaction–diffusion systems Kutniv, M. aut Włoch, A. aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 58(2019), 3 vom: 26. Nov., Seite 612-631 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:58 year:2019 number:3 day:26 month:11 pages:612-631 https://doi.org/10.1007/s10910-019-01089-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 AR 58 2019 3 26 11 612-631 |
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10.1007/s10910-019-01089-y doi (DE-627)OLC2060427037 (DE-He213)s10910-019-01089-y-p DE-627 ger DE-627 rakwb eng 510 540 VZ Datsko, B. verfasserin (orcid)0000-0002-9700-669X aut Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature Switzerland AG 2019 Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented. Mathematical modeling Autocatalytic chemical reaction Self-organization phenomena Anomalous diffusion Reaction–diffusion systems Kutniv, M. aut Włoch, A. aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 58(2019), 3 vom: 26. Nov., Seite 612-631 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:58 year:2019 number:3 day:26 month:11 pages:612-631 https://doi.org/10.1007/s10910-019-01089-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 AR 58 2019 3 26 11 612-631 |
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Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented. © Springer Nature Switzerland AG 2019 |
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Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented. © Springer Nature Switzerland AG 2019 |
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Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. It is shown that stability of steady-state solutions and their subsequent evolution are mainly determined by the eigenvalue spectrum of a linearized system and level of anomalous diffusion (orders of fractional derivatives). The results of linear stability analysis are confirmed by computer simulations. To illustrate the influence of anomalous diffusion on stability properties and possible dynamics in fractional reaction–diffusion systems, we generalized two classical activator–inhibitor nonlinear models: FitzHugh–Nagumo and Brusselator. Based on them a common picture of typical nonlinear solutions in nonlinear incommensurate time-fractional activator–inhibitor systems is presented. © Springer Nature Switzerland AG 2019 |
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10.1007/s10910-019-01089-y |
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2024-07-04T01:19:05.759Z |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2060427037</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230511063122.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2019 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10910-019-01089-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2060427037</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10910-019-01089-y-p</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="a">540</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Datsko, B.</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-9700-669X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</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">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Nature Switzerland AG 2019</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Auto-wave solutions in nonlinear time-fractional reaction–diffusion systems are investigated. 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