Wang and Wong perceptual decision making model

wang_wong_simplified.py

"""
Wang and Wong 2006 perceptual decision making model

adapted from  https://github.com/xjwanglab/book/blob/b0a8e775a9f687cefbcbb4fcbe3fc19b6343bd70/wong2006/wong2006.py  # noqa
"""
import numpy as np
import matplotlib.pyplot as plt


def run(coherence=.3):
    NT = 4000
    t_plot = np.arange(NT)
    t_stim = (t_plot > 100) * (t_plot < 1000)
    mean_stim = np.ones(NT)*0.0104
    diff_stim = mean_stim*coherence
    Istim = np.array([(mean_stim + diff_stim) * t_stim,
                      (mean_stim - diff_stim) * t_stim])

    # Initialize S1 and S
    S = np.zeros((2, NT))
    r = np.zeros((2, NT))
    S[:, 0] = .1

    # Loop over time points in a trial
    for t in xrange(NT-1):
        # Firing ratea
        I0 = 0.3255
        gE = 0.2609
        gI = -0.0497

        def F(I, a=270., b=108., d=0.154):
            # Relu
            return (a*I - b)/(1.-np.exp(-d*(a*I - b)))

        r[0, t] = F(gE*S[0, t] + gI*S[1, t] + Istim[0, t] + I0)
        r[1, t] = F(gE*S[1, t] + gI*S[0, t] + Istim[1, t] + I0)

        # Mean NMDA-mediated synaptic dynamics updating
        gamma = 0.641 * 0.0005
        S[:, t+1] = S[:, t] * (.995 - gamma*r[:, t]) + gamma*r[:, t]
    return r, S


coherences = (.1, .3, .5, .9)
cmap = plt.get_cmap('viridis')
colors = cmap(np.linspace(0, 1, len(coherences)))
fig, axes = plt.subplots(2, 1)
for coherence, color in zip(coherences, colors):
    r, S = run(coherence)
    axes[0].plot(S[0], color=color)
    axes[0].plot(S[1], color=color, linestyle=':')
    axes[1].plot(r[0], color=color)
    axes[1].plot(r[1], color=color, linestyle=':')
plt.show()