tvb.Generic2dOscillator

experimental.network_dynamics.dynamics.tvb.Generic2dOscillator(**kwargs)

Generic 2D oscillator with configurable nullclines.

A flexible two-variable dynamical system where V typically represents a fast variable (e.g., membrane potential) and W a slow recovery variable. The model can exhibit FitzHugh-Nagumo dynamics, bistability, or other behaviors depending on parameters.

Notes

State equations:

\[ \begin{aligned} \frac{dV}{dt} &= d \tau (-f V^3 + e V^2 + g V + \alpha W + \gamma I + \gamma c_{\text{delayed}} + \gamma c_{\text{instant}}) + I_{\text{stim}} \\ \frac{dW}{dt} &= \frac{d}{\tau} (a + b V + c V^2 - \beta W) \end{aligned} \]

The parameter drive \(I\) is scaled by \(d \tau\) along with the rest of the vector field, while the external input \(I_{\text{stim}}\) is added outside it, in raw derivative units. This mirrors TVB, where the stimulus is applied by the integrator rather than inside the model.

Parameter regimes:

• Excitable (FitzHugh-Nagumo-like): \(a=-2.0, b=-10.0, c=0.0, d=0.02, I=0.0\)
• Bistable: \(a=1.0, b=0.0, c=-5.0, d=0.02, I=0.0\)
• Morris-Lecar-like: \(a=0.5, b=0.6, c=-4.0, d=0.02, I=0.0\)

Attributes

Name	Type	Description
STATE_NAMES	tuple of str	State variables: ('V', 'W') (fast and slow variables)
INITIAL_STATE	tuple of float	Default initial conditions: (0.0, 0.0)
COUPLING_INPUTS	dict	Coupling specification: {'instant': 1, 'delayed': 1}
DEFAULT_PARAMS	Bunch	Configurable nullcline parameters

References

FitzHugh (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1, 445.

Methods

Name	Description
dynamics	Compute Generic2dOscillator dynamics.

dynamics

experimental.network_dynamics.dynamics.tvb.Generic2dOscillator.dynamics(
    t,
    state,
    params,
    coupling,
    external,
)

Compute Generic2dOscillator dynamics.

Args: t: Current time state: State [2, n_nodes] with (V, W) params: Model parameters coupling: Coupling inputs (.instant, .delayed)

Returns: derivatives: [2, n_nodes] state derivatives