Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation
Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualita...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Paraskevov, Alexander [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990, 110(2022), 2 vom: 13. Aug., Seite 1823-1829 |
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| Übergeordnetes Werk: |
volume:110 ; year:2022 ; number:2 ; day:13 ; month:08 ; pages:1823-1829 |
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| DOI / URN: |
10.1007/s11071-022-07708-9 |
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SPR048410640 |
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| 520 | |a Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. | ||
| 650 | 4 | |a Morris–Lecar model |7 (dpeaa)DE-He213 | |
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| 650 | 4 | |a Time-delay system |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Delay differential equation |7 (dpeaa)DE-He213 | |
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10.1007/s11071-022-07708-9 doi (DE-627)SPR048410640 (SPR)s11071-022-07708-9-e DE-627 ger DE-627 rakwb eng Paraskevov, Alexander verfasserin (orcid)0000-0001-7847-5194 aut Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. Morris–Lecar model (dpeaa)DE-He213 Neuronal excitability (dpeaa)DE-He213 Constant current stimulation (dpeaa)DE-He213 Periodic spiking (dpeaa)DE-He213 Time-delay system (dpeaa)DE-He213 Delay differential equation (dpeaa)DE-He213 Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 110(2022), 2 vom: 13. Aug., Seite 1823-1829 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:110 year:2022 number:2 day:13 month:08 pages:1823-1829 https://dx.doi.org/10.1007/s11071-022-07708-9 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2022 2 13 08 1823-1829 |
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10.1007/s11071-022-07708-9 doi (DE-627)SPR048410640 (SPR)s11071-022-07708-9-e DE-627 ger DE-627 rakwb eng Paraskevov, Alexander verfasserin (orcid)0000-0001-7847-5194 aut Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. Morris–Lecar model (dpeaa)DE-He213 Neuronal excitability (dpeaa)DE-He213 Constant current stimulation (dpeaa)DE-He213 Periodic spiking (dpeaa)DE-He213 Time-delay system (dpeaa)DE-He213 Delay differential equation (dpeaa)DE-He213 Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 110(2022), 2 vom: 13. Aug., Seite 1823-1829 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:110 year:2022 number:2 day:13 month:08 pages:1823-1829 https://dx.doi.org/10.1007/s11071-022-07708-9 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2022 2 13 08 1823-1829 |
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10.1007/s11071-022-07708-9 doi (DE-627)SPR048410640 (SPR)s11071-022-07708-9-e DE-627 ger DE-627 rakwb eng Paraskevov, Alexander verfasserin (orcid)0000-0001-7847-5194 aut Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. Morris–Lecar model (dpeaa)DE-He213 Neuronal excitability (dpeaa)DE-He213 Constant current stimulation (dpeaa)DE-He213 Periodic spiking (dpeaa)DE-He213 Time-delay system (dpeaa)DE-He213 Delay differential equation (dpeaa)DE-He213 Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 110(2022), 2 vom: 13. Aug., Seite 1823-1829 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:110 year:2022 number:2 day:13 month:08 pages:1823-1829 https://dx.doi.org/10.1007/s11071-022-07708-9 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2022 2 13 08 1823-1829 |
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10.1007/s11071-022-07708-9 doi (DE-627)SPR048410640 (SPR)s11071-022-07708-9-e DE-627 ger DE-627 rakwb eng Paraskevov, Alexander verfasserin (orcid)0000-0001-7847-5194 aut Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. Morris–Lecar model (dpeaa)DE-He213 Neuronal excitability (dpeaa)DE-He213 Constant current stimulation (dpeaa)DE-He213 Periodic spiking (dpeaa)DE-He213 Time-delay system (dpeaa)DE-He213 Delay differential equation (dpeaa)DE-He213 Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 110(2022), 2 vom: 13. Aug., Seite 1823-1829 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:110 year:2022 number:2 day:13 month:08 pages:1823-1829 https://dx.doi.org/10.1007/s11071-022-07708-9 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2022 2 13 08 1823-1829 |
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10.1007/s11071-022-07708-9 doi (DE-627)SPR048410640 (SPR)s11071-022-07708-9-e DE-627 ger DE-627 rakwb eng Paraskevov, Alexander verfasserin (orcid)0000-0001-7847-5194 aut Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. Morris–Lecar model (dpeaa)DE-He213 Neuronal excitability (dpeaa)DE-He213 Constant current stimulation (dpeaa)DE-He213 Periodic spiking (dpeaa)DE-He213 Time-delay system (dpeaa)DE-He213 Delay differential equation (dpeaa)DE-He213 Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 110(2022), 2 vom: 13. Aug., Seite 1823-1829 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:110 year:2022 number:2 day:13 month:08 pages:1823-1829 https://dx.doi.org/10.1007/s11071-022-07708-9 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 110 2022 2 13 08 1823-1829 |
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Paraskevov, Alexander |
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Paraskevov, Alexander misc Morris–Lecar model misc Neuronal excitability misc Constant current stimulation misc Periodic spiking misc Time-delay system misc Delay differential equation Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation |
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Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation Morris–Lecar model (dpeaa)DE-He213 Neuronal excitability (dpeaa)DE-He213 Constant current stimulation (dpeaa)DE-He213 Periodic spiking (dpeaa)DE-He213 Time-delay system (dpeaa)DE-He213 Delay differential equation (dpeaa)DE-He213 |
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Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation |
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analog of the hutchinson equation in biophysical neurodynamics: from the morris–lecar model to a delay differential equation |
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Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation |
| abstract |
Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. © The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
| abstractGer |
Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. © The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
| abstract_unstemmed |
Abstract Starting with the classical biophysical Morris–Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type. © The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
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Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris–Lecar model to a delay differential equation |
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