amat2_psc_exp - Non-resetting leaky integrate-and-fire neuron model
with exponential PSCs and adaptive threshold.
amat2_psc_exp is an implementation of a leaky integrate-and-fire model
with exponential shaped postsynaptic currents (PSCs). Thus, postsynaptic
currents have an infinitely short rise time.
The threshold is lifted when the neuron is fired and then decreases in a
fixed time scale toward a fixed level [3].
The threshold crossing is followed by a total refractory period
during which the neuron is not allowed to fire, even if the membrane
potential exceeds the threshold. The membrane potential is NOT reset,
but continuously integrated.
The linear subthresold dynamics is integrated by the Exact
Integration scheme [1]. The neuron dynamics is solved on the time
grid given by the computation step size. Incoming as well as emitted
spikes are forced to that grid.
An additional state variable and the corresponding differential
equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with
neuron like dynamics interacting by point events is described in
[1]. A flow chart can be found in [2].
The following parameters can be set in the status dictionary:
\verbatim embed:rst
=========== ======= ===========================================================
C_m pF Capacity of the membrane
E_L mV Resting potential
tau_m ms Membrane time constant
tau_syn_ex ms Time constant of postsynaptic excitatory currents
tau_syn_in ms Time constant of postsynaptic inhibitory currents
t_ref ms Duration of absolute refractory period (no spiking)
V_m mV Membrane potential
I_e pA Constant input current
t_spike ms Point in time of last spike
tau_1 ms Short time constant of adaptive threshold [3, eqs 2-3]
tau_2 ms Long time constant of adaptive threshold [3, eqs 2-3]
alpha_1 mV Amplitude of short time threshold adaption [3, eqs 2-3]
alpha_2 mV Amplitude of long time threshold adaption [3, eqs 2-3]
tau_v ms Time constant of kernel for voltage-dependent threshold
component [3, eqs 16-17]
beta 1/ms Scaling coefficient for voltage-dependent threshold
component [3, eqs 16-17]
omega mV Resting spike threshold (absolute value, not
relative to E_L as in [3])
=========== ======= ===========================================================
=========== ==== =======================================================
**State variables that can be read out with the multimeter device**
------------------------------------------------------------------------
V_m mV Non-resetting membrane potential
V_th mV Two-timescale adaptive threshold
=========== ==== =======================================================
\endverbatim
SpikeEvent, CurrentEvent, DataLoggingRequest
SpikeEvent
\f$ \tau_m != \tau_{syn_{ex,in}} \f$ is required by the current implementation to
avoid a degenerate case of the ODE describing the model [1].
For very similar values, numerics will be unstable.
\verbatim embed:rst
.. [1] Rotter S, Diesmann M (1999). Exact simulation of
time-invariant linear systems with applications to neuronal
modeling. Biologial Cybernetics 81:381-402.
DOI: https://doi.org/10.1007/s004220050570
.. [2] Diesmann M, Gewaltig M-O, Rotter S, & Aertsen A (2001). State
space analysis of synchronous spiking in cortical neural
networks. Neurocomputing 38-40:565-571.
DOI: https://doi.org/10.1016/S0925-2312(01)00409-X
.. [3] Kobayashi R, Tsubo Y and Shinomoto S (2009). Made-to-order
spiking neuron model equipped with a multi-timescale adaptive
threshold. Frontiers in Computational Neuroscience, 3:9.
DOI: https://dx.doi.org/10.3389%2Fneuro.10.009.2009
.. [4] Yamauchi S, Kim H, Shinomoto S (2011). Elemental spiking neuron model
for reproducing diverse firing patterns and predicting precise
firing times. Frontiers in Computational Neuroscience, 5:42.
DOI: https://doi.org/10.3389/fncom.2011.00042
\endverbatim
Thomas Heiberg & Hans E. Plesser (modified mat2_psc_exp model of
Thomas Pfeil)
April 2013
/var/www/debian/nest/nest-simulator-2.18.0/models/amat2_psc_exp.h