dynamicalab.dynamics.ThetaModelDynamics

class dynamicalab.dynamics.ThetaModelDynamics(sigma=0.1, input_intensity=0.5, cos_transform=True)

Theta model, or Ermentrout–Kopell canonical model, is a biological neuron model.

\[ \begin{align}\begin{aligned}\dfrac{dx_i}{dt} = 1-\cos(x_i) + [1+\cos(x_i)]\eta_j\\\eta_j = \Big[I + \dfrac{\sigma}{N}\sum_{j=1}^N w_{ij}(1-\cos(x_j))\Big]\end{aligned}\end{align} \]

Since the activity is interpreted as an angle, it is typical to take the cosinus of the activity.

__init__(sigma=0.1, input_intensity=0.5, cos_transform=True)

Initialization.

Parameters

sigma : Float : (default=0.1)

input_intensity : Float : (default=0.5)

Input intensity to each node.

cos_transform : Bool : (default=True)

If true, take the cosinus of the activity as output.

Methods

__init__([sigma, input_intensity, cos_transform])	Initialization.
best_x0(G)	Random numbers between 0 and 2*np.pi