DualExpon

class brainpy.state.DualExpon(in_size, name=None, tau_decay=Quantity(10., "ms"), tau_rise=Quantity(1., "ms"), amplitude=1.0, normalize=True, g_initializer=Constant(value=0. mS))

Dual exponential synapse model.

This class implements a synapse model with separate rise and decay time constants, which produces a more biologically realistic conductance waveform than a single exponential model. The model is characterized by the differential equation system:

dg_rise/dt = -g_rise/tau_rise dg_decay/dt = -g_decay/tau_decay g = a * (g_decay - g_rise)

where \(a\) is a scaling factor for the output waveform.

Parameters:

• in_size (Size) – Size of the input.

• name (str, optional) – Name of the synapse instance.

• tau_decay (ArrayLike, default 10.0*u.ms) – Time constant of decay in milliseconds.

• tau_rise (ArrayLike, default 1.0*u.ms) – Time constant of rise in milliseconds.

• normalize (bool, default True) – Whether to use peak normalization for the dual-exponential waveform.

• amplitude (ArrayLike, default 1.) – Output amplitude scaling factor. When normalize=True, the waveform is peak-normalized to 1 and then scaled by amplitude. When normalize=False, the raw difference waveform is scaled directly by amplitude.

• g_initializer (ArrayLike or Callable, default init.Constant(0. * u.mS)) – Initial value or initializer for synaptic conductance.

g_rise

Rise component of synaptic conductance.

Type:

HiddenState

g_decay

Decay component of synaptic conductance.

Type:

HiddenState

tau_rise

Time constant of rise phase.

Type:

Parameter

tau_decay

Time constant of decay phase.

Type:

Parameter

normalize

Whether peak normalization is enabled.

Type:

bool

amplitude

Output amplitude scaling factor.

Type:

Parameter

See also

Expon

Single-exponential decay synapse.

Alpha

Alpha-function synapse (special case where tau_rise == tau_decay).

Notes

The dual exponential model produces a conductance waveform that is more physiologically realistic than a simple exponential decay, with a finite rise time followed by a slower decay.

The implementation uses an exponential Euler integration method. The output of this synapse is the difference between decay and rise components, optionally peak-normalized and scaled by amplitude.

If normalize=True, the peak of the waveform is normalized to amplitude. If normalize=False, the raw waveform is scaled directly by amplitude.

This class inherits from AlignPost, which means it can be used in projection patterns where synaptic variables are aligned with post-synaptic neurons, enabling event-driven computation and more efficient handling of sparse connectivity patterns.

References

[1]

Roth, A., & van Rossum, M. C. W. (2009). Modeling synapses. In Computational Modeling Methods for Neuroscientists (pp. 139-160). MIT Press.

Examples

>>> import brainstate
>>> import saiunit as u
>>> import brainpy
>>> with brainstate.environ.context(dt=0.1 * u.ms):
...     syn = brainpy.state.DualExpon(in_size=1, tau_rise=0.5 * u.ms, tau_decay=5.0 * u.ms)
...     syn.init_state()
...     T, t0 = 300, 50
...     g = []
...     for t in range(T):
...         x = (1.0 * u.mS if t == t0 else 0.0 * u.mS)
...         y = u.get_magnitude(syn.update(x=x) / u.mS)
...         g.append(float(y[0]))

init_state(batch_size=None, **kwargs)

State initialization function.

reset_state(batch_size=None, **kwargs)

State resetting function.