tvb.CoombesByrne2D

experimental.network_dynamics.dynamics.tvb.CoombesByrne2D(**kwargs)

Coombes-Byrne 2D infinite theta neuron population model.

Two-dimensional mean field model with conductance-based synaptic interactions, derived via the Ott-Antonsen reduction. Unlike the Montbrio-Pazo-Roxin model, this includes implicit synaptic conductance proportional to firing rate.

Notes

State variables:

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

Synaptic conductance:

\[g = \kappa \pi r\]

where \(\kappa\) is the synaptic conductance scaling factor.

State equations:

\[ \begin{aligned} \frac{dr}{dt} &= \frac{\Delta}{\pi} + 2Vr - gr^2 \\ \frac{dV}{dt} &= V^2 - (\pi r)^2 + \eta + (v_{\text{syn}} - V)g + c_{\text{coup}} \end{aligned} \]

where \(c_{\text{coup}}\) is the combined instant and delayed coupling.

The conductance \(g = \kappa \pi r\) creates a quadratic nonlinearity in the firing rate equation, leading to different dynamical regimes compared to the standard Montbrio-Pazo-Roxin model.

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)
AUXILIARY_NAMES	tuple of str	Auxiliary variable: ('g',) (synaptic conductance)
COUPLING_INPUTS	dict	Coupling specification: {'instant': 1, 'delayed': 1}
DEFAULT_PARAMS	Bunch	Standard Coombes-Byrne parameters

References

Coombes & Byrne (2019). Next generation neural mass models. In Nonlinear Dynamics in Computational Neuroscience (pp. 1-16). Springer.

Methods

Name	Description
dynamics	Compute Coombes-Byrne 2D dynamics.

dynamics

experimental.network_dynamics.dynamics.tvb.CoombesByrne2D.dynamics(
    t,
    state,
    params,
    coupling,
    external,
)

Compute Coombes-Byrne 2D dynamics.

Parameters

Name	Type	Description	Default
t	float	Current time	required
state	jnp.ndarray	Current state with shape [2, n_nodes] containing (r, V)	required
params	Bunch	Model parameters	required
coupling	Bunch	Coupling inputs with attributes: - .instant[0]: local r-coupling - .delayed[0]: long-range r-coupling	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 [1, n_nodes] containing synaptic conductance g