MATHEMATICAL CONSTANTS · d(phi_i)/dt

Read the equation

This relation defines d(phi_i)/dt in the source section “MATHEMATICAL CONSTANTS · d(phi_i)/dt”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read d(phi_i)/dt as the quantity being defined or updated by this relation.

2. Evaluates oscillatory sine or cosine terms using the stated phase or frequency.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

        update_metrics();
    }

    /**
     * Kuramoto phase dynamics step
     *
     * d(phi_i)/dt = omega_i + (K/N) * sum_j sin(phi_j - phi_i)
     */
    void step(double dt) {
        std::array<double, N> dphases;

        for (size_t i = 0; i < N; ++i) {
            double sum_coupling = 0;
            for (size_t j = 0; j < N; ++j) {
                sum_coupling += coupling[i][j] * std::sin(phases[j] - phases[i]);
            }
            dphases[i] = 2 * M_PI * natural_freqs[i] + coupling_strength * sum_coupling;

d(phi_i)/dt = omega_i + (K/N) * sum_j sin(phi_j - phi_i)

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