brainpy.dyn.synapses.DualExpCUBA
brainpy.dyn.synapses.DualExpCUBA#
- class brainpy.dyn.synapses.DualExpCUBA(pre, post, conn, conn_type='dense', g_max=1.0, tau_decay=10.0, tau_rise=1.0, delay_step=None, method='exp_auto', name=None)[source]#
Current-based 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:
\[\begin{split}\begin{aligned} &g_{\mathrm{syn}}(t)=g_{\mathrm{max}} g \\ &\frac{d g}{d t}=-\frac{g}{\tau_{\mathrm{decay}}}+h \\ &\frac{d h}{d t}=-\frac{h}{\tau_{\text {rise }}}+ \delta\left(t_{0}-t\right), \end{aligned}\end{split}\]The current onto the post-synaptic neuron is given by
\[I_{syn}(t) = g_{\mathrm{syn}}(t).\]Model Examples
>>> import brainpy as bp >>> import matplotlib.pyplot as plt >>> >>> neu1 = bp.dyn.LIF(1) >>> neu2 = bp.dyn.LIF(1) >>> syn1 = bp.dyn.DualExpCUBA(neu1, neu2, bp.connect.All2All()) >>> 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', '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()
(Source code, png, hires.png, pdf)
- 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.
conn_type (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_decay (float, JaxArray, JaxArray, ndarray) – The time constant of the synaptic decay phase. [ms]
tau_rise (float, JaxArray, JaxArray, ndarray) – The time constant of the synaptic rise phase. [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.
- 2
Roth, A., & Van Rossum, M. C. W. (2009). Modeling Synapses. Computational Modeling Methods for Neuroscientists.
- __init__(pre, post, conn, conn_type='dense', g_max=1.0, tau_decay=10.0, tau_rise=1.0, delay_step=None, method='exp_auto', name=None)[source]#
Methods
__init__
(pre, post, conn[, conn_type, ...])check_post_attrs
(*attrs)Check whether post group satisfies the requirement.
check_pre_attrs
(*attrs)Check whether pre group satisfies the requirement.
dg
(g, t, h)dh
(h, t)get_delay_data
(name, delay_step, *indices)Get delay data according to the provided delay steps.
ints
([method])Collect all integrators in this node and the children nodes.
load_states
(filename[, verbose])Load the model states.
nodes
([method, level, include_self])Collect all children nodes.
output
(g_post)register_delay
(name, delay_step, delay_target)Register delay variable.
register_implicit_nodes
(nodes)register_implicit_vars
(variables)reset
()Reset function which reset the whole variables in the model.
reset_delay
(name, delay_target)Reset the delay variable.
save_states
(filename[, variables])Save the model states.
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
(t, dt)The function to specify the updating rule.
update_delay
(name, delay_data)Update the delay according to the delay data.
vars
([method, level, include_self])Collect all variables in this node and the children nodes.
Attributes
global_delay_vars
name
steps