Expon

Expon#

class brainpy.dyn.Expon(size, keep_size=False, sharding=None, method='exp_auto', name=None, mode=None, tau=8.0)[source]#

Exponential decay synapse model.

Model Descriptions

The single exponential decay synapse model assumes the release of neurotransmitter, its diffusion across the cleft, the receptor binding, and channel opening all happen very quickly, so that the channels instantaneously jump from the closed to the open state. Therefore, its expression is given by

\[g_{\mathrm{syn}}(t)=g_{\mathrm{max}} e^{-\left(t-t_{0}\right) / \tau}\]

where \(\tau_{delay}\) is the time constant of the synaptic state decay, \(t_0\) is the time of the pre-synaptic spike, \(g_{\mathrm{max}}\) is the maximal conductance.

Accordingly, the differential form of the exponential synapse is given by

\[\begin{aligned} & \frac{d g}{d t} = -\frac{g}{\tau_{decay}}+\sum_{k} \delta(t-t_{j}^{k}). \end{aligned}\]

This module can be used with interface brainpy.dyn.ProjAlignPreMg2, as shown in the following example:

import numpy as np
import brainpy as bp
import brainpy.math as bm

import matplotlib.pyplot as plt


class ExponSparseCOBA(bp.Projection):
    def __init__(self, pre, post, delay, prob, g_max, tau, E):
        super().__init__()

        self.proj = bp.dyn.ProjAlignPreMg2(
            pre=pre,
            delay=delay,
            syn=bp.dyn.Expon.desc(pre.num, tau=tau),
            comm=bp.dnn.CSRLinear(bp.conn.FixedProb(prob, pre=pre.num, post=post.num), g_max),
            out=bp.dyn.COBA(E=E),
            post=post,
        )


class SimpleNet(bp.DynSysGroup):
    def __init__(self, syn_cls, E=0.):
        super().__init__()
        self.pre = bp.dyn.SpikeTimeGroup(1, indices=(0, 0, 0, 0), times=(10., 30., 50., 70.))
        self.post = bp.dyn.LifRef(1, V_rest=-60., V_th=-50., V_reset=-60., tau=20., tau_ref=5.,
                                  V_initializer=bp.init.Constant(-60.))
        self.syn = syn_cls(self.pre, self.post, delay=None, prob=1., g_max=1., tau=5., E=E)

    def update(self):
        self.pre()
        self.syn()
        self.post()
        # monitor the following variables
        conductance = self.syn.proj.refs['syn'].g
        current = self.post.sum_inputs(self.post.V)
        return conductance, current, self.post.V

Moreover, it can also be used with interface ProjAlignPostMg2:

class ExponSparseCOBAPost(bp.Projection):
    def __init__(self, pre, post, delay, prob, g_max, tau, E):
        super().__init__()

        self.proj = bp.dyn.ProjAlignPostMg2(
            pre=pre,
            delay=delay,
            comm=bp.dnn.EventCSRLinear(bp.conn.FixedProb(prob, pre=pre.num, post=post.num), g_max),
            syn=bp.dyn.Expon.desc(post.num, tau=tau),
            out=bp.dyn.COBA.desc(E=E),
            post=post,
        )

Parameters:

tau (Union[float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Callable]) – float. The time constant of decay. [ms]
size (Union[int, Sequence[int]]) – int, or sequence of int. The neuronal population size.
sharding (Optional[Sequence[str]]) – The sharding strategy.
keep_size (bool) – bool. Keep the neuron group size.
mode (Optional[Mode]) – Mode. The computing mode.
name (Optional[str]) – str. The group name.

update(x=None)[source]#: The function to specify the updating rule.

Expon

Contents

Expon#