# brainmodels.synapses.AlphaCUBA

class brainmodels.synapses.AlphaCUBA(pre, post, conn, delay=0.0, g_max=1.0, tau_decay=10.0, method='exponential_euler', **kwargs)[source]

Current-based alpha synapse model.

Model Descriptions

The analytical expression of alpha synapse is given by:

$g_{syn}(t)= g_{max} \frac{t-t_{s}}{\tau} \exp \left(-\frac{t-t_{s}}{\tau}\right).$

While, this equation is hard to implement. So, let’s try to convert it into the differential forms:

\begin{split}\begin{aligned} &g_{\mathrm{syn}}(t)= g_{\mathrm{max}} g \\ &\frac{d g}{d t}=-\frac{g}{\tau}+h \\ &\frac{d h}{d t}=-\frac{h}{\tau}+\delta\left(t_{0}-t\right) \end{aligned}\end{split}

The current onto the post-synaptic neuron is given by

$I_{syn}(t) = g_{\mathrm{syn}}(t).$

Model Examples

Model Parameters

 Parameter Init Value Unit Explanation delay 0 ms The decay length of the pre-synaptic spikes. tau_decay 2 ms The decay time constant of the synaptic state. g_max .2 µmho(µS) The maximum conductance.

Model Variables

 Variables name Initial Value Explanation g 0 Synapse conductance on the post-synaptic neuron. h 0 Gating variable. pre_spike False The history spiking states of the pre-synaptic neurons.

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, delay=0.0, g_max=1.0, tau_decay=10.0, method='exponential_euler', **kwargs)[source]

Methods

 __init__(pre, post, conn[, delay, g_max, ...]) build_inputs([inputs, show_code]) build_monitors([show_code]) cpu() cuda() derivative(g, h, t) ints([method]) Collect all integrators in this node and the children nodes. jax_update(_t, _dt) load_states(filename[, verbose, check]) Load the model states. nodes([method, _paths]) Collect all children nodes. numpy_update(_t, _dt) register_constant_delay(key, size, delay[, ...]) Register a constant delay. run(duration[, dt, report, inputs, extra_func]) The running function. save_states(filename[, all_vars]) Save the model states. step(t_and_dt, **kwargs) to(devices) tpu() train_vars([method]) The shortcut for retrieving all trainable variables. unique_name([name, type]) Get the unique name for this object. update(*args, **kwargs) The function to specify the updating rule. vars([method]) Collect all variables in this node and the children nodes.

Attributes

 implicit_nodes Used to wrap the implicit children nodes which cannot be accessed by self.xxx implicit_vars Used to wrap the implicit variables which cannot be accessed by self.xxx target_backend Used to specify the target backend which the model to run.