tvb.MontbrioPazoRoxin

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

Montbrio-Pazo-Roxin infinite theta neuron population model.

Two-dimensional mean field model describing the Ott-Antonsen reduction of infinite all-to-all coupled quadratic integrate-and-fire (QIF) neurons.

Notes

State variables:

• \(r\): Average firing rate of the population
• \(V\): Average membrane potential of the population

State equations:

\[ \begin{aligned} \frac{dr}{dt} &= \frac{1}{\tau} \left(\frac{\Delta}{\pi \tau} + 2Vr\right) \\ \frac{dV}{dt} &= \frac{1}{\tau} \left(V^2 - (\pi \tau r)^2 + \eta + J\tau r + I + c_r c_{\text{coup},r} + c_v c_{\text{coup},V}\right) \end{aligned} \]

where \(c_{\text{coup},r}\) and \(c_{\text{coup},V}\) are the combined instant and delayed coupling components, and \(c_r\), \(c_v\) are coupling weights.

The model has 2-dimensional coupling allowing independent coupling through firing rate (r) and membrane potential (V).

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variables: ('r', 'V')
INITIAL_STATE	tuple of float	Default initial conditions: (0.1, 0.0)
COUPLING_INPUTS	dict	Coupling specification: {'instant': 2, 'delayed': 2}
DEFAULT_PARAMS	Bunch	Standard parameters for QIF neuron population

References

Montbrio, Pazo & Roxin (2015). Macroscopic description for networks of spiking neurons. Physical Review X, 5(2), 021028.

Methods

Name	Description
dynamics	Compute Montbrio-Pazo-Roxin dynamics.

dynamics

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

Compute Montbrio-Pazo-Roxin dynamics.

Args: t: Current time state: State [2, n_nodes] with (r, V) params: Model parameters coupling: Coupling inputs - .instant[0]: local r-coupling - .instant[1]: local V-coupling - .delayed[0]: long-range r-coupling - .delayed[1]: long-range V-coupling

Returns: derivatives: [2, n_nodes] state derivatives