tvb.JansenRit

experimental.network_dynamics.dynamics.tvb.JansenRit(**kwargs)

Jansen-Rit neural mass model with multi-coupling support.

This implementation accepts two coupling inputs (instantaneous and delayed), both of which add into the excitatory interneuron population equation.

Notes

The model describes the dynamics of three neural populations: pyramidal cells, excitatory interneurons, and inhibitory interneurons.

State equations:

\[ \begin{aligned} \frac{dy_0}{dt} &= y_3 \\ \frac{dy_3}{dt} &= A a S(y_1 - y_2) - 2a y_3 - a^2 y_0 \\ \frac{dy_1}{dt} &= y_4 \\ \frac{dy_4}{dt} &= A a (\mu + a_2 J S(a_1 J y_0) + c_{\text{instant}} + c_{\text{delayed}}) - 2a y_4 - a^2 y_1 \\ \frac{dy_2}{dt} &= y_5 \\ \frac{dy_5}{dt} &= B b (a_4 J S(a_3 J y_0)) - 2b y_5 - b^2 y_2 \end{aligned} \]

Sigmoid function:

\[S(v) = \frac{2 \nu_{\text{max}}}{1 + \exp(r(v_0 - v))}\]

State variables:

• \(y_0\): Average membrane potential of pyramidal cells
• \(y_1\): Average membrane potential of excitatory interneurons
• \(y_2\): Average membrane potential of inhibitory interneurons
• \(y_3, y_4, y_5\): Time derivatives of \(y_0, y_1, y_2\)

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variable names: ("y0", "y1", "y2", "y3", "y4", "y5")
INITIAL_STATE	tuple of float	Default initial conditions: (0.0, 5.0, 5.0, 0.0, 0.0, 0.0)
COUPLING_INPUTS	dict	Coupling input specification: {'instant': 1, 'delayed': 1}
DEFAULT_PARAMS	Bunch	Standard Jansen-Rit parameters (A, B, a, b, v0, nu_max, r, J, a_1-a_4, mu)

Methods

Name	Description
dynamics	Compute Jansen-Rit dynamics with two coupling inputs.

dynamics

experimental.network_dynamics.dynamics.tvb.JansenRit.dynamics(
    t,
    state,
    params,
    coupling,
    external,
)

Compute Jansen-Rit dynamics with two coupling inputs.

Parameters

Name	Type	Description	Default
t	float	Current time (unused for autonomous system)	required
state	jnp.ndarray	Current state with shape [6, n_nodes] containing (y0, y1, y2, y3, y4, y5)	required
params	Bunch	Model parameters including: A, B, a, b, v0, nu_max, r, J, a_1, a_2, a_3, a_4, mu	required
coupling	Bunch	Coupling inputs with attributes .instant[1, n_nodes] and .delayed[1, n_nodes]	required
external	Bunch	External inputs (currently unused)	required

Returns

Name	Type	Description
derivatives	jnp.ndarray	State derivatives with shape [6, n_nodes]
auxiliaries	jnp.ndarray	Auxiliary variables with shape [3, n_nodes] containing sigmoid function values