tvb.ReducedWongWang

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

Reduced Wong-Wang neural mass model with multi-coupling support.

This implementation accepts two coupling inputs (instantaneous and delayed), both of which contribute to the total synaptic input.

Notes

The model describes the dynamics of a single synaptic gating variable representing NMDA receptor activity.

State equation:

\[\frac{dS}{dt} = -\frac{S}{\tau_s} + (1-S) H(x) \gamma\]

Transfer function:

\[H(x) = \frac{ax - b}{1 - \exp(-d(ax - b))}\]

Total input:

\[x = w J_N S + I_o + J_N (c_{\text{instant}} + c_{\text{delayed}})\]

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variable name: ("S",) (synaptic gating variable)
INITIAL_STATE	tuple of float	Default initial condition: (0.1,)
AUXILIARY_NAMES	tuple of str	Auxiliary variable: ("H",) (transfer function output)
COUPLING_INPUTS	dict	Coupling specification: {'instant': 1, 'delayed': 1}
DEFAULT_PARAMS	Bunch	Standard Wong-Wang parameters (a, b, d, gamma, tau_s, w, J_N, I_o)

Methods

Name	Description
dynamics	Compute Wong-Wang dynamics with two coupling inputs.

dynamics

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

Compute Wong-Wang 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 [1, n_nodes] containing S (synaptic gating variable)	required
params	Bunch	Model parameters: a, b, d, gamma, tau_s, w, J_N, I_o	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 [1, n_nodes] containing dS/dt
auxiliaries	jnp.ndarray	Auxiliary variables with shape [1, n_nodes] containing H (transfer function)