tvb.LarterBreakspear

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

Larter-Breakspear neural mass model.

A modified Morris-Lecar model with three state variables representing pyramidal cells, potassium dynamics, and inhibitory interneurons. The model exhibits rich dynamical behaviors including fixed points, limit cycles, and chaos.

Notes

State variables:

• \(V\): Membrane potential of pyramidal cells
• \(W\): Potassium channel gating variable
• \(Z\): Inhibitory interneuron activity

Dynamical regimes:

• \(d_V < 0.55\): Fixed point dynamics
• \(0.55 < d_V < 0.59\): Limit cycle attractors
• \(d_V > 0.59\): Chaotic attractors

Auxiliary variables:

\[ \begin{aligned} Q_V &= \frac{1}{2} Q_{V,\text{max}} \left(1 + \tanh\left(\frac{V - V_T}{d_V}\right)\right) \quad \text{(pyramidal firing rate)} \\ Q_Z &= \frac{1}{2} Q_{Z,\text{max}} \left(1 + \tanh\left(\frac{Z - Z_T}{d_Z}\right)\right) \quad \text{(inhibitory firing rate)} \\ m_{\text{Ca}} &= \frac{1}{2} \left(1 + \tanh\left(\frac{V - T_{\text{Ca}}}{d_{\text{Ca}}}\right)\right) \quad \text{(Ca channel gating)} \end{aligned} \]

with similar expressions for \(m_{\text{Na}}\) and \(m_K\).

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variables: ('V', 'W', 'Z')
INITIAL_STATE	tuple of float	Default initial conditions: (0.0, 0.0, 0.0)
AUXILIARY_NAMES	tuple of str	Auxiliary variables: ('QV', 'QZ', 'm_Ca', 'm_Na', 'm_K')
COUPLING_INPUTS	dict	Coupling specification: {'instant': 1, 'delayed': 1}
DEFAULT_PARAMS	Bunch	Conductances, thresholds, and synaptic weights

References

Breakspear et al. (2003). Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics. Network: Computation in Neural Systems, 14, 703-732.

Methods

Name	Description
dynamics	Compute Larter-Breakspear dynamics.

dynamics

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

Compute Larter-Breakspear dynamics.

Parameters

Name	Type	Description	Default
t	float	Current time (ms)	required
state	jnp.ndarray	Current state with shape [3, n_nodes] containing (V, W, Z)	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 [3, n_nodes]
auxiliaries	jnp.ndarray	Auxiliary variables with shape [5, n_nodes] containing (QV, QZ, m_Ca, m_Na, m_K)