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.