Quasi-discreted dynamics of a neural net: The lighthouse model
This paper studies the features of a net of pulse-coupled model neurons, taking into account the dynamics of dendrites and axons. The axonal pulses are modelled by δ-functions. In the case of small damping of dendritic currents, the model can be treated exactly and explicitly. Because of the δ-funct...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S1026022600000182 |
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| _version_ | 1832567354399129600 |
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| author | Hermann Haken |
| author_facet | Hermann Haken |
| author_sort | Hermann Haken |
| collection | DOAJ |
| description | This paper studies the features of a net of pulse-coupled model neurons, taking into account the dynamics of dendrites and axons. The axonal pulses are modelled by δ-functions. In the case of small damping of dendritic currents, the model can be treated exactly and explicitly. Because of the δ-functions, the phase-equations can be converted into algebraic equations at discrete times. We first exemplify our procedure by two neurons, and then present the results for N neurons. We admit a general dependence of input and coupling strengths on the
neuronal indices. In detail, the results are |
| format | Article |
| id | doaj-art-0cecda44d1284ac697aa68a94e83363d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-0cecda44d1284ac697aa68a94e83363d2025-02-03T01:01:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2000-01-014318720010.1155/S1026022600000182Quasi-discreted dynamics of a neural net: The lighthouse modelHermann Haken0Institute for Theoretical Physics 1, Center of Synergetics, Pfaffenwaldring 57/4, Stuttgart D-70550, GermanyThis paper studies the features of a net of pulse-coupled model neurons, taking into account the dynamics of dendrites and axons. The axonal pulses are modelled by δ-functions. In the case of small damping of dendritic currents, the model can be treated exactly and explicitly. Because of the δ-functions, the phase-equations can be converted into algebraic equations at discrete times. We first exemplify our procedure by two neurons, and then present the results for N neurons. We admit a general dependence of input and coupling strengths on the neuronal indices. In detail, the results arehttp://dx.doi.org/10.1155/S1026022600000182Neural netsDiscrete dynamicsPhase-lockingFluctuations. |
| spellingShingle | Hermann Haken Quasi-discreted dynamics of a neural net: The lighthouse model Discrete Dynamics in Nature and Society Neural nets Discrete dynamics Phase-locking Fluctuations. |
| title | Quasi-discreted dynamics of a neural net: The lighthouse model |
| title_full | Quasi-discreted dynamics of a neural net: The lighthouse model |
| title_fullStr | Quasi-discreted dynamics of a neural net: The lighthouse model |
| title_full_unstemmed | Quasi-discreted dynamics of a neural net: The lighthouse model |
| title_short | Quasi-discreted dynamics of a neural net: The lighthouse model |
| title_sort | quasi discreted dynamics of a neural net the lighthouse model |
| topic | Neural nets Discrete dynamics Phase-locking Fluctuations. |
| url | http://dx.doi.org/10.1155/S1026022600000182 |
| work_keys_str_mv | AT hermannhaken quasidiscreteddynamicsofaneuralnetthelighthousemodel |