siegert_neuron – model for mean-field analysis of spiking networks ================================================================== Description +++++++++++ ``siegert_neuron`` is an implementation of a rate model with the non-linearity given by the gain function of the leaky-integrate-and-fire neuron with delta or exponentially decaying synapses [2]_ and [3]_ (their eq. 25). The model can be used for a mean-field analysis of spiking networks. A constant mean input can be provided to create neurons with a target rate, e.g. to model a constant external input. The model supports connections to other rate models with zero delay, and uses the secondary_event concept introduced with the gap-junction framework. For details on the numerical solution of the Siegert integral, you can check out the `Siegert_neuron_integration <../model_details/siegert_neuron_integration.ipynb>`_ notebook in the NEST source code. See also [1]_, [4]_. Parameters ++++++++++ The following parameters can be set in the status dictionary. ===== ====== ============================== rate 1/s Rate (1/s) tau ms Time constant mean 1/s Additional constant input ===== ====== ============================== The following parameters can be set in the status directory and are used in the evaluation of the gain function. Parameters as in iaf_psc_exp/delta. ========= ====== ================================================ tau_m ms Membrane time constant tau_syn ms Time constant of postsynaptic currents t_ref ms Duration of refractory period theta mV Threshold relative to resting potential V_reset mV Reset relative to resting potential ========= ====== ================================================ References ++++++++++ .. [1] Hahne J, Dahmen D, Schuecker J, Frommer A, Bolten M, Helias M, Diesmann M (2017). Integration of continuous-time dynamics in a spiking neural network simulator. Frontiers in Neuroinformatics, 11:34. DOI: https://doi.org/10.3389/fninf.2017.00034 .. [2] Fourcaud N, Brunel N (2002). Dynamics of the firing probability of noisy integrate-and-fire neurons, Neural Computation, 14(9):2057-2110 DOI: https://doi.org/10.1162/089976602320264015 .. [3] Schuecker J, Diesmann M, Helias M (2015). Modulated escape from a metastable state driven by colored noise. Physical Review E 92:052119 DOI: https://doi.org/10.1103/PhysRevE.92.052119 .. [4] Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M (2015). A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations. Frontiers in Neuroinformatics, 9:22. DOI: https://doi.org/10.3389/fninf.2015.00022 Sends +++++ DiffusionConnectionEvent Receives ++++++++ DiffusionConnectionEvent, DataLoggingRequest See also ++++++++ :doc:`Neuron `, :doc:`Rate `