**Name:**

amat2_psc_exp - Non-resetting leaky integrate-and-fire neuron model

with exponential PSCs and adaptive threshold.

**Description:**

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].

**Parameters:**

The following parameters can be set in the status dictionary:

C_m double - Capacity of the membrane in pF

E_L double - Resting potential in mV

tau_m double - Membrane time constant in ms

tau_syn_ex double - Time constant of postsynaptic excitatory currents in ms

tau_syn_in double - Time constant of postsynaptic inhibitory currents in ms

t_ref double - Duration of absolute refractory period (no spiking) in

ms

V_m double - Membrane potential in mV

I_e double - Constant input current in pA

t_spike double - Point in time of last spike in ms

tau_1 double - Short time constant of adaptive threshold in ms

[3, eqs 2-3]

tau_2 double - Long time constant of adaptive threshold in ms

[3, eqs 2-3]

alpha_1 double - Amplitude of short time threshold adaption in mV

[3, eqs 2-3]

alpha_2 double - Amplitude of long time threshold adaption in mV

[3, eqs 2-3]

tau_v double - Time constant of kernel for voltage-dependent threshold

component in ms [3, eqs 16-17]

beta double - Scaling coefficient for voltage-dependent threshold

component in 1/ms [3, eqs 16-17]

omega double - Resting spike threshold in mV (absolute value, not

relative to E_L as in [3])

The following state variables can be read out with the multimeter device:

V_m Non-resetting membrane potential

V_th Two-timescale adaptive threshold

**Receives:**

SpikeEvent, CurrentEvent, DataLoggingRequest

**Sends:**

SpikeEvent

**Remarks:**

tau_m != tau_syn_{ex,in} 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.

**References:**

[1] Rotter S & Diesmann M (1999) Exact simulation of

time-invariant linear systems with applications to neuronal

modeling. Biologial Cybernetics 81:381-402.

[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.

[3] Kobayashi R, Tsubo Y and Shinomoto S (2009) Made-to-order

spiking neuron model equipped with a multi-timescale adaptive

threshold. Front. Comput. Neurosci. 3:9. doi:10.3389/neuro.10.009.2009

[4] Yamauchi S, Kim H and Shinomoto S (2011) Elemental spiking neuron model

for reproducing diverse firing patterns and predicting precise

firing times. Front. Comput. Neurosci. 5:42.

doi: 10.3389/fncom.2011.00042

**Author:**

Thomas Heiberg & Hans E. Plesser (modified mat2_psc_exp model of

Thomas Pfeil)

**FirstVersion:**

April 2013

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/models/amat2_psc_exp.h