models.py

"""
Set of spiking neural models.
"""


import ipywidgets as widgets
import numpy as np

from model_base import BaseSpikingModel

IZHIKEVICH_MODEL_SLIDERS = {
    "a": widgets.FloatSlider(
        min=0.02, max=0.1, step=0.008, value=0.02, description="a"
    ),
    "b": widgets.FloatSlider(
        min=0.2, max=0.25, step=0.01, value=0.2, description="b"
    ),
    "c": widgets.IntSlider(
        min=-65, max=-50, step=5, value=-65, description="c"
    ),
    "d": widgets.FloatSlider(
        min=0.05, max=8.0, step=0.1, value=8.0, description="d"
    ),
}


class IzhikevichModel(BaseSpikingModel):
    """
    Izhikevich model of spiking neuron.

    Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE
        Transactions on neural networks, 14(6), 1569-1572.
    """

    y0 = [-70.0, -14.0]
    index_voltage_variable = 0
    spike_condition = 30.0  # mV
    required_params = ["a", "b", "c", "d"]

    def _apply_reset(self, y):
        """
        Spike reset for model:
        v <- c
        u <- u + d
        """
        y[0] = self.params["c"]
        y[1] += self.params["d"]
        return y

    def _rhs(self, t, y, I):
        """
        Right hand side of the equation:
        v' = 0.04*v^2 + 5*v + 140 - u + I
        u' = a*(b*v - u)
        """
        v, u = y
        t_idx = int(t / self.dt)
        v_deriv = 0.04 * np.power(v, 2) + 5.0 * v + 140.0 - u + I[t_idx]
        u_deriv = self.params["a"] * (self.params["b"] * v - u)
        return (v_deriv, u_deriv)