mercurial.core.hopf module

Hopf oscillator for amplitude dynamics and state transitions (Section 22).

class mercurial.core.hopf.HopfNetwork(n_oscillators: int, alphas: List[float] | None = None, omegas: List[float] | None = None, beta: float = 1.0, sigma: float = 0.05, kuramoto_coupling: float = 0.0, diffusive_coupling: float = 0.0)

Bases: object

Network of Hopf oscillators with Kuramoto phase coupling and diffusive amplitude coupling.

Methods

get_mean_amplitude
get_order_parameter
step

get_mean_amplitude() → float

get_order_parameter() → Tuple[float, float]

step(dt: float) → None

class mercurial.core.hopf.HopfOscillator(params: HopfParams | None = None, frequency_band: str = 'alpha', **kwargs)

Bases: object

Single Hopf oscillator: dz/dt = (α + iω)z - β|z|²z + noise.

Methods

derivative
get_amplitude
get_phase
set_bifurcation
step

derivative(z: complex) → complex

get_amplitude() → float

get_phase() → float

set_bifurcation(alpha: float) → None

step(dt: float, external_input: complex = 0.0) → None