braintools.input.exponential_decay

braintools.input.exponential_decay#

braintools.input.exponential_decay(amplitude, tau, duration, t_start=None, t_end=None)#

Generate exponentially decaying input.

Creates an input that decays exponentially from an initial amplitude. Useful for modeling synaptic currents or adaptation processes.

Parameters:

  • amplitude (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Initial amplitude of the exponential decay. Supports current units.

  • tau (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Time constant of the exponential decay. Supports time units.

  • duration (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Total duration of the input signal.

  • t_start (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – Start time of the decay. Before this, current is 0. Default is 0.

  • t_end (Array | ndarray | bool | number | bool | int | float | complex | Quantity | None) – End time of the decay. After this, current is 0. Default is duration.

Returns:

current – The exponentially decaying input.

Return type:

ndarray or Quantity

Examples

>>> import brainunit as u
>>> import brainstate
>>> brainstate.environ.set(dt=0.1 * u.ms)

Simple exponential decay

>>> current = exponential_decay(
...     amplitude=10 * u.pA,
...     tau=20 * u.ms,
...     duration=100 * u.ms
... )

Fast decay (mimicking AMPA receptor)

>>> current = exponential_decay(
...     amplitude=1 * u.nA,
...     tau=2 * u.ms,
...     duration=20 * u.ms
... )

Slow decay (mimicking NMDA receptor)

>>> current = exponential_decay(
...     amplitude=0.5 * u.nA,
...     tau=100 * u.ms,
...     duration=500 * u.ms
... )

Delayed decay

>>> current = exponential_decay(
...     amplitude=5 * u.pA,
...     tau=10 * u.ms,
...     duration=100 * u.ms,
...     t_start=20 * u.ms,  # Start decay at 20ms
...     t_end=80 * u.ms      # End at 80ms
... )

Notes

  • The decay follows: I(t) = amplitude * exp(-t/tau)

  • At t=tau, the current is amplitude/e (~37% of initial)

  • At t=3*tau, the current is ~5% of initial amplitude