pyhctsa.operations.physics.force_potential

pyhctsa.operations.physics.force_potential(y, what_potential='dblwell', params=None)

Couple a time series to a driven dynamical system.

The input time series acts as an external forcing term on a simulated particle evolving in a specified potential well.

Two potential functions are available:

  1. Quartic double-well potential

\[V(x) = \frac{x^4}{4} - \frac{\alpha^2 x^2}{2},\]

with corresponding force

\[F(x) = -\frac{dV}{dx} = -x^3 + \alpha^2 x.\]

  1. Sinusoidal potential

\[V(x) = -\cos\left(\frac{x}{\alpha}\right),\]

with corresponding force

\[F(x) = \frac{1}{\alpha} \sin\left(\frac{x}{\alpha}\right).\]

The time series provides a forcing contribution to the particle dynamics, which are integrated numerically.

Parameters:
y : array-like

Input time series.

what_potential : str, optional

Potential function to simulate.

  • "dblwell": Quartic double-well potential.

  • "sine": Sinusoidal potential.

params : list of float, optional

Simulation parameters in the form [alpha, kappa, deltat].

  • alpha: Controls the well separation ("dblwell") or the

oscillation period ("sine"). - kappa: Friction (damping) coefficient. - deltat: Integration time step.

Returns:

Summary statistics of the simulated trajectory, including mean, range, proportion of positive values, zero-crossing rate, autocorrelation, final position, and standard deviation.

Return type:

dict