Resonance

Module Resonance — resonance detection for the parametrisation method.

Choosing a resonance style

Four constructors are provided; choose based on the problem type:

• resonance_set_from_graph_style (default for non-autonomous SSMs): Detects internal resonances relative to the master-mode eigenvalue combination s = Σ kᵢ λᵢ, plus autonomous/forced external resonances. Use for mechanical systems with harmonic forcing or whenever an external eigenvalue (forcing frequency) is present.

• resonance_set_from_complex_normal_form_style (autonomous ROMs, complex form): Targets only near-identity monomials; suitable for computing autonomous SSMs when all reduced variables are complex conjugate pairs.

• resonance_set_from_real_normal_form_style (autonomous ROMs, real form): Variant of CNF style operating on real eigenvalue pairs; use when building a real-valued reduced-order model without explicit complex conjugation.

• resonance_set_from_condition_number_estimate (near-resonance uncertainty): Flags a monomial as resonant when the cohomological operator is nearly singular (condition number exceeds a threshold). Use when eigenvalues are approximate or when the resonance gap is small and purely geometric criteria are unreliable.