STDP

models.Synapses.STDP(
    self,
    tau_plus=20.0,
    tau_minus=20.0,
    A_plus=0.01,
    A_minus=0.01,
    w_min=0.0,
    w_max=1.0,
)

Spike-timing dependent plasticity, online version.

Song, S., and Abbott, L.F. (2001). Cortical development and remapping through spike timing-dependent plasticity. Neuron 32, 339-350.

Parameters (global):

• tau_plus = 20.0 : time constant of the pre-synaptic trace (ms)
• tau_minus = 20.0 : time constant of the pre-synaptic trace (ms)
• A_plus = 0.01 : increase of the pre-synaptic trace after a spike.
• A_minus = 0.01 : decrease of the post-synaptic trace after a spike.
• w_min = 0.0 : minimal value of the weight w.
• w_max = 1.0 : maximal value of the weight w.

Variables:

• x : pre-synaptic trace:

tau_plus  * dx/dt = -x

• y: post-synaptic trace:

tau_minus * dy/dt = -y

Both variables are evaluated event-driven.

Pre-spike events:

g_target += w

x += A_plus * w_max

w = clip(w + y, w_min , w_max)

Post-spike events::

y -= A_minus * w_max

w = clip(w + x, w_min , w_max)

Equivalent code:

STDP = ann.Synapse(
    parameters = """
        tau_plus = 20.0 : projection
        tau_minus = 20.0 : projection
        A_plus = 0.01 : projection
        A_minus = 0.01 : projection
        w_min = 0.0 : projection
        w_max = 1.0 : projection
    """,
    equations = """
        tau_plus  * dx/dt = -x : event-driven
        tau_minus * dy/dt = -y : event-driven
    """,
    pre_spike="""
        g_target += w
        x += A_plus * w_max
        w = clip(w + y, w_min , w_max)
    """,
    post_spike="""
        y -= A_minus * w_max
        w = clip(w + x, w_min , w_max)
    """
)