On the Uniqueness of Participation Factors in Nonlinear Dynamical Systems

The paper proves that nonlinear participation factors (PFs) are invariant under left/right eigenvector rescalings once all θ-factors are fixed (Theorem 2), by explicitly eliminating σ- and ξ-dependence in equations (20)–(21) and concluding dependence only on θ; the model independently proves the same sufficiency via a gauge-equivariance argument for the Poincaré–Dulac normal-form construction. The paper’s text contains a wording glitch stating “if and only if” in the paragraph after (21), but immediately clarifies in Remark 5 that the condition is sufficient (not necessary), aligning with the model’s claim of invariance given fixed θ. See Theorem 2 and (20a)–(21b) and the sufficiency-only statements and examples in the surrounding discussion and conclusion .