tvb.Epileptor

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

Epileptor model for epileptic seizure dynamics.

Six-dimensional model with two coupled populations operating on different time scales, designed to reproduce transitions between interictal (between seizures) and ictal (during seizure) states.

Notes

The model consists of:

• Population 1 (x1, y1, z): Fast time scale, represents rapid ictal activity
• Population 2 (x2, y2): Ultra-slow time scale, controls interictal background
• Filter variable g: Low-pass filtered version of x1

State equations:

\[ \begin{aligned} \frac{dx_1}{dt} &= t_t (y_1 - z + I_{\text{ext}} + K_{vf} c_{\text{pop1}} + f_1(x_1,x_2) x_1) \\ \frac{dy_1}{dt} &= t_t (c - d x_1^2 - y_1) \\ \frac{dz}{dt} &= t_t r (h(x_1,z) - z + K_s c_{\text{pop1}}) \\ \frac{dx_2}{dt} &= t_t (-y_2 + x_2 - x_2^3 + I_{\text{ext2}} + bb \cdot g - 0.3(z-3.5) + K_f c_{\text{pop2}}) \\ \frac{dy_2}{dt} &= t_t \frac{-y_2 + f_2(x_2)}{\tau} \\ \frac{dg}{dt} &= t_t (-0.01(g - 0.1 x_1)) \end{aligned} \]

where \(f_1\), \(f_2\), and \(h\) are piecewise nonlinear functions modeling different dynamical regimes.

Key parameters:

• \(x_0\): Epileptogenicity parameter (controls seizure threshold)
• \(K_{vf}, K_f, K_s\): Coupling strengths at different time scales
• modification: If True, uses nonlinear (sigmoidal) permittivity

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variables: ('x1', 'y1', 'z', 'x2', 'y2', 'g')
INITIAL_STATE	tuple of float	Default initial conditions: (-1.5, -10.0, 3.5, -1.0, 0.0, 0.0)
COUPLING_INPUTS	dict	Coupling specification: {'instant': 2, 'delayed': 2} Components [0] couple to population 1 (fast), [1] to population 2 (slow)
DEFAULT_PARAMS	Bunch	Standard Epileptor parameters from Jirsa et al. 2014

References

Jirsa et al. (2014). On the nature of seizure dynamics. Brain, 137(8), 2210-2230.

Methods

Name	Description
dynamics	Compute Epileptor dynamics.

dynamics

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

Compute Epileptor dynamics.

Parameters

Name	Type	Description	Default
t	float	Current time	required
state	jnp.ndarray	Current state with shape [6, n_nodes] containing (x1, y1, z, x2, y2, g)	required
params	Bunch	Model parameters	required
coupling	Bunch	Coupling inputs with attributes: - .instant[0], .delayed[0]: population 1 coupling - .instant[1], .delayed[1]: population 2 coupling	required
external	Bunch	External inputs (currently unused)	required

Returns

Name	Type	Description
derivatives	jnp.ndarray	State derivatives with shape [6, n_nodes]