# 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, A=None, method='exp_auto', name=None, mode=None, stop_spike_gradient=False)[source]#

Dual exponential synapse model.

Model Descriptions

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

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

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} &\frac{d g}{d t}=-\frac{g}{\tau_{\mathrm{decay}}}+h \\ &\frac{d h}{d t}=-\frac{h}{\tau_{\text {rise }}}+ (\frac{1}{\tau_{\text{rise}}} - \frac{1}{\tau_{\text{decay}}}) A \delta\left(t_{0}-t\right), \end{aligned}\end{split}

By default, $$A$$ has the following value:

$A = \frac{{\tau }_{decay}}{{\tau }_{decay}-{\tau }_{rise}}{\left(\frac{{\tau }_{rise}}{{\tau }_{decay}}\right)}^{\frac{{\tau }_{rise}}{{\tau }_{rise}-{\tau }_{decay}}}$

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)
>>> 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.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.

__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, A=None, method='exp_auto', name=None, mode=None, stop_spike_gradient=False)[source]#

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[, label, category]) 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) 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_current_inputs(*args[, init, label]) Summarize all current inputs by the defined input functions .current_inputs. sum_delta_inputs(*args[, init, label]) Summarize all delta inputs by the defined input functions .delta_inputs. sum_inputs(*args, **kwargs) 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

 after_updates before_updates cur_inputs current_inputs delta_inputs g_max implicit_nodes implicit_vars 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.