tvb.WongWangExcInh

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

Wong-Wang neural mass model with excitatory and inhibitory populations.

Two-population model representing local excitatory-inhibitory dynamics with NMDA-mediated recurrence and long-range coupling.

Notes

State equations:

\[ \begin{aligned} x_e &= w_p J_N S_e - J_i S_i + W_e I_o + c_{\text{total}} + I_{\text{ext}} \\ H_e &= \frac{a_e x_e - b_e}{1 - \exp(-d_e(a_e x_e - b_e))} \\ \frac{dS_e}{dt} &= -\frac{S_e}{\tau_e} + (1 - S_e) H_e \gamma_e \end{aligned} \]

\[ \begin{aligned} x_i &= J_N S_e - S_i + W_i I_o + \lambda c_{\text{total}} \\ H_i &= \frac{a_i x_i - b_i}{1 - \exp(-d_i(a_i x_i - b_i))} \\ \frac{dS_i}{dt} &= -\frac{S_i}{\tau_i} + H_i \gamma_i \end{aligned} \]

where: \(c_{\text{total}} = G J_N (c_{\text{delayed}} + c_{\text{instant}})\)

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variables: ('S_e', 'S_i') (excitatory and inhibitory synaptic gating)
INITIAL_STATE	tuple of float	Default initial conditions: (0.001, 0.001)
AUXILIARY_NAMES	tuple of str	Auxiliary variables: ('H_e', 'H_i') (transfer functions)
COUPLING_INPUTS	dict	Coupling specification: {'instant': 1, 'delayed': 1}
DEFAULT_PARAMS	Bunch	Standard Wong-Wang parameters for excitatory/inhibitory populations

References

Wong & Wang (2006). A Recurrent Network Mechanism of Time Integration in Perceptual Decisions. Journal of Neuroscience, 26(4), 1314-1328.

Methods

Name	Description
dynamics	Compute Wong-Wang excitatory-inhibitory dynamics.

dynamics

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

Compute Wong-Wang excitatory-inhibitory dynamics.

Parameters

Name	Type	Description	Default
t	float	Current time (ms)	required
state	jnp.ndarray	Current state with shape [2, n_nodes] containing (S_e, S_i)	required
params	Bunch	Model parameters	required
coupling	Bunch	Coupling inputs with attributes .instant and .delayed	required
external	Bunch	External inputs (currently unused)	required

Returns

Name	Type	Description
derivatives	jnp.ndarray	State derivatives with shape [2, n_nodes]
auxiliaries	jnp.ndarray	Auxiliary variables with shape [2, n_nodes] containing (H_e, H_i) transfer functions