tvb.Linear

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

Linear neural mass model with damping.

Single-state variable model representing simple damped linear dynamics, useful for testing, debugging, and understanding basic coupling mechanisms without nonlinear complications.

Notes

State equation:

\[\frac{dx}{dt} = \gamma x + c_{\text{delayed}} + c_{\text{instant}}\]

where:

• \(x\): State variable
• \(\gamma\): Damping coefficient (must be negative for stability)
• \(c_{\text{delayed}}\): Long-range coupling input
• \(c_{\text{instant}}\): Local coupling input (proportional to x)

The damping coefficient \(\gamma\) should be negative and its magnitude should exceed the node’s in-degree to ensure stability. For \(\gamma > 0\), the system will exhibit exponential growth.

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variable: ('x',)
INITIAL_STATE	tuple of float	Default initial condition: (0.01,)
AUXILIARY_NAMES	tuple of str	No auxiliary variables: ()
COUPLING_INPUTS	dict	Coupling specification: {'instant': 1, 'delayed': 1}
DEFAULT_PARAMS	Bunch	Damping coefficient gamma=-10.0 (must be negative for stability)

Methods

Name	Description
dynamics	Compute linear dynamics.

dynamics

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

Compute linear dynamics.

Parameters

Name	Type	Description	Default
t	float	Current time	required
state	jnp.ndarray	Current state with shape [1, n_nodes] containing x	required
params	Bunch	Model parameters (gamma: damping coefficient)	required
coupling	Bunch	Coupling inputs with attributes: - .instant[0]: local coupling - .delayed[0]: long-range coupling	required
external	Bunch	External inputs (currently unused)	required

Returns

Name	Type	Description
derivatives	jnp.ndarray	State derivative with shape [1, n_nodes]