brainpy.synapses.DualExponential

class brainpy.synapses.DualExponential(pre, post, conn, stp=None, output=None, comp_method='dense', g_max=1.0, tau_decay=10.0, tau_rise=1.0, delay_step=None, method='exp_auto', name=None, mode=None, stop_spike_gradient=False)

Dual exponential synapse model.

Model Descriptions

The dual exponential synapse model [1], also named as difference of two exponentials model, is given by:

\[g_{\mathrm{syn}}(t)=g_{\mathrm{max}} \frac{\tau_{1} \tau_{2}}{ \tau_{1}-\tau_{2}}\left(\exp \left(-\frac{t-t_{0}}{\tau_{1}}\right) -\exp \left(-\frac{t-t_{0}}{\tau_{2}}\right)\right)\]

where \(\tau_1\) is the time constant of the decay phase, \(\tau_2\) is the time constant of the rise phase, \(t_0\) is the time of the pre-synaptic spike, \(g_{\mathrm{max}}\) is the maximal conductance.

However, in practice, this formula is hard to implement. The equivalent solution is two coupled linear differential equations [2]:

\[\begin{split}\begin{aligned} &g_{\mathrm{syn}}(t)=g_{\mathrm{max}} g * \mathrm{STP} \\ &\frac{d g}{d t}=-\frac{g}{\tau_{\mathrm{decay}}}+h \\ &\frac{d h}{d t}=-\frac{h}{\tau_{\text {rise }}}+ \delta\left(t_{0}-t\right), \end{aligned}\end{split}\]

where \(\mathrm{STP}\) is used to model the short-term plasticity effect of synapses.

Model Examples

>>> import brainpy as bp
>>> from brainpy import neurons, synapses, synouts
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = neurons.LIF(1)
>>> neu2 = neurons.LIF(1)
>>> syn1 = synapses.DualExponential(neu1, neu2, bp.connect.All2All(), output=synouts.CUBA())
>>> net = bp.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.DSRunner(net, inputs=[('pre.input', 25.)], monitors=['pre.V', 'post.V', 'syn.g', 'syn.h'])
>>> runner.run(150.)
>>>
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8)
>>> fig.add_subplot(gs[0, 0])
>>> 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()
>>>
>>> fig.add_subplot(gs[1, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.g'], label='g')
>>> plt.plot(runner.mon.ts, runner.mon['syn.h'], label='h')
>>> plt.legend()
>>> plt.show()

Parameters:

• pre (NeuDyn) – The pre-synaptic neuron group.

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

• conn (optional, ArrayType, 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, ArrayType, Initializer, Callable) – The delay length. It should be the value of \(\mathrm{delay\_time / dt}\).

• tau_decay (float, ArrayArray, ndarray) – The time constant of the synaptic decay phase. [ms]

• tau_rise (float, ArrayArray, ndarray) – The time constant of the synaptic rise phase. [ms]

• g_max (float, ArrayType, 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.

[2]

Roth, A., & Van Rossum, M. C. W. (2009). Modeling Synapses. Computational Modeling Methods for Neuroscientists.

__init__(pre, post, conn, stp=None, output=None, comp_method='dense', g_max=1.0, tau_decay=10.0, tau_rise=1.0, delay_step=None, method='exp_auto', name=None, mode=None, stop_spike_gradient=False)

Methods

__init__(pre, post, conn[, stp, output, ...])
add_aft_update(key, fun)	Add the after update into this node
add_bef_update(key, fun)	Add the before update into this node
add_inp_fun(key, fun)	Add an input function.
check_post_attrs(*attrs)	Check whether post group satisfies the requirement.
check_pre_attrs(*attrs)	Check whether pre group satisfies the requirement.
clear_input(*args, **kwargs)	Empty function of clearing inputs.
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
get_aft_update(key)	Get the after update of this node by the given key.
get_bef_update(key)	Get the before update of this node by the given key.
get_delay_data(identifier, delay_pos, *indices)	Get delay data according to the provided delay steps.
get_delay_var(name)
get_inp_fun(key)	Get the input function.
get_local_delay(var_name, delay_name)	Get the delay at the given identifier (name).
has_aft_update(key)	Whether this node has the after update of the given key.
has_bef_update(key)	Whether this node has the before update of the given key.
jit_step_run(i, *args, **kwargs)	The jitted step function for running.
load_state(state_dict, **kwargs)	Load states from a dictionary.
load_state_dict(state_dict[, warn, compatible])	Copy parameters and buffers from state_dict into this module and its descendants.
nodes([method, level, include_self])	Collect all children nodes.
register_delay(identifier, delay_step, ...)	Register delay variable.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables[, var_cls])
register_local_delay(var_name, delay_name[, ...])	Register local relay at the given delay time.
reset(*args, **kwargs)	Reset function which reset the whole variables in the model (including its children models).
reset_local_delays([nodes])	Reset local delay variables.
reset_state(*args, **kwargs)	Reset function which resets local states in this model.
save_state(**kwargs)	Save states as a dictionary.
setattr(key, value)	rtype: None
state_dict(**kwargs)	Returns a dictionary containing a whole state of the module.
step_run(i, *args, **kwargs)	The step run function.
sum_inputs(*args[, init, label])	Summarize all inputs by the defined input functions .cur_inputs.
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
tracing_variable(name, init, shape[, ...])	Initialize the variable which can be traced during computations and transformations.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
tree_flatten()	Flattens the object as a PyTree.
tree_unflatten(aux, dynamic_values)	Unflatten the data to construct an object of this class.
unique_name([name, type_])	Get the unique name for this object.
update([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

g_max
mode	Mode of the model, which is useful to control the multiple behaviors of the model.
name	Name of the model.
supported_modes	Supported computing modes.
cur_inputs