# brainpy.dyn.synapses.Exponential#

class brainpy.dyn.synapses.Exponential(pre, post, conn, output=CUBA, stp=None, comp_method='sparse', g_max=1.0, delay_step=None, tau=8.0, method='exp_auto', name=None, mode=NormalMode, stop_spike_gradient=False)[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{split}\begin{aligned} & g_{\mathrm{syn}}(t) = g_{max} g * \mathrm{STP} \\ & \frac{d g}{d t} = -\frac{g}{\tau_{decay}}+\sum_{k} \delta(t-t_{j}^{k}). \end{aligned}\end{split}

where $$\mathrm{STP}$$ is used to model the short-term plasticity effect.

Model Examples

>>> import brainpy as bp
>>> from brainpy.dyn import neurons, synapses, synouts
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = neurons.LIF(1)
>>> neu2 = neurons.LIF(1)
>>> syn1 = synapses.Exponential(neu1, neu2, bp.conn.All2All(),
>>>                             g_max=5., output=synouts.CUBA())
>>> net = bp.dyn.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.dyn.DSRunner(net, inputs=[('pre.input', 25.)], monitors=['pre.V', 'post.V', 'syn.g'])
>>> runner.run(150.)
>>>
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8)
>>> plt.plot(runner.mon.ts, runner.mon['pre.V'], label='pre-V')
>>> plt.plot(runner.mon.ts, runner.mon['post.V'], label='post-V')
>>> plt.legend()
>>>
>>> plt.plot(runner.mon.ts, runner.mon['syn.g'], label='g')
>>> plt.legend()
>>> plt.show()

Parameters
• pre (NeuGroup) – The pre-synaptic neuron group.

• post (NeuGroup) – The post-synaptic neuron group.

• conn (optional, ndarray, JaxArray, dict of (str, ndarray), TwoEndConnector) – The synaptic connections.

• comp_method (str) – The connection type used for model speed optimization. It can be sparse and dense. The default is sparse.

• delay_step (int, ndarray, JaxArray, Initializer, Callable) – The delay length. It should be the value of $$\mathrm{delay\_time / dt}$$.

• tau (float, JaxArray, ndarray) – The time constant of decay. [ms]

• g_max (float, ndarray, JaxArray, Initializer, Callable) – The synaptic strength (the maximum conductance). Default is 1.

• name (str) – The name of this synaptic projection.

• method (str) – The numerical integration methods.

References

1

Sterratt, David, Bruce Graham, Andrew Gillies, and David Willshaw. “The Synapse.” Principles of Computational Modelling in Neuroscience. Cambridge: Cambridge UP, 2011. 172-95. Print.

__init__(pre, post, conn, output=CUBA, stp=None, comp_method='sparse', g_max=1.0, delay_step=None, tau=8.0, method='exp_auto', name=None, mode=NormalMode, stop_spike_gradient=False)[source]#

Methods

 __init__(pre, post, conn[, output, stp, ...]) check_post_attrs(*attrs) Check whether post group satisfies the requirement. check_pre_attrs(*attrs) Check whether pre group satisfies the requirement. clear_input() get_delay_data(identifier, delay_step, *indices) Get delay data according to the provided delay steps. init_weights(weight, comp_method[, sparse_data]) rtype Union[float, TypeVar(Array, JaxArray, Variable, TrainVar, Array, ndarray)] load_states(filename[, verbose]) Load the model states. nodes([method, level, include_self]) Collect all children nodes. offline_fit(target, fit_record) offline_init() online_fit(target, fit_record) online_init() register_delay(identifier, delay_step, ...) Register delay variable. register_implicit_nodes(*nodes, **named_nodes) register_implicit_vars(*variables, ...) reset([batch_size]) Reset function which reset the whole variables in the model. reset_local_delays([nodes]) Reset local delay variables. reset_state([batch_size]) Reset function which reset the states in the model. save_states(filename[, variables]) Save the model states. syn2post_with_all2all(syn_value, syn_weight) syn2post_with_dense(syn_value, syn_weight, ...) syn2post_with_one2one(syn_value, syn_weight) train_vars([method, level, include_self]) The shortcut for retrieving all trainable variables. unique_name([name, type_]) Get the unique name for this object. update(tdi[, pre_spike]) The function to specify the updating rule. update_local_delays([nodes]) Update local delay variables. vars([method, level, include_self]) Collect all variables in this node and the children nodes.

Attributes

 global_delay_data mode Mode of the model, which is useful to control the multiple behaviors of the model. name Name of the model.