  In modal analysis and control of a nonlinear dynamical system, participation
factors of state variables with respect to a mode of interest serve as pivotal
tools for stability studies. Linear participation factors are uniquely
determined by the mode's shape and composition, which are defined by the right
and left eigenvectors of the linearized model. For nonlinear participation
factors as well as five other variants of participation factors, this paper
finds the sufficient conditions for them to be unique against scaling factors
on the shape and composition of a mode. Besides, the similarity between the
scaling factor and perturbation amplitude is also discussed.
