Struct KuramotoModel 

pub struct KuramotoModel {
    pub omega: Vec<f64>,
    pub k: f64,
}

Kuramoto model of coupled oscillators.

dθ_i/dt = ω_i + (K/N) Σ_j sin(θ_j - θ_i)

The order parameter r = |Σ e^{iθ_j}| / N measures synchrony.

Fields

omega: Vec<f64>

Natural frequencies ω_i.

k: f64

Coupling strength K.

Implementations

impl KuramotoModel

pub fn new(omega: Vec<f64>, k: f64) -> Self

Creates a Kuramoto model from natural frequencies and coupling K.

pub fn lorentzian(n: usize, omega0: f64, gamma_width: f64, seed: u64) -> Self

Generates Lorentzian-distributed (Cauchy) natural frequencies.

Mean omega0, half-width gamma. Critical coupling K_c = 2γ.

pub fn n(&self) -> usize

Number of oscillators.

pub fn order_parameter(phases: &[f64]) -> f64

Computes the order parameter r ∈ [0, 1].

r = |1/N Σ e^{iθ_j}|

pub fn mean_phase(phases: &[f64]) -> f64

Mean phase angle (argument of the complex order parameter).

pub fn integrate( &self, phases0: &[f64], dt: f64, steps: usize, ) -> (Vec<f64>, Vec<f64>)

Integrates for steps using RK4 with step dt.

Returns trajectory of order parameters.

pub fn critical_coupling_estimate(&self) -> f64

Estimated critical coupling K_c = 2 / (π g(0)) for Lorentzian with width γ → K_c = 2γ.

For a general distribution approximated by the frequency spread σ: K_c ≈ 2σ/√π.