Displacement of the birth-type boundary by third-harmonic corrections

Determine whether the third-harmonic correction displaces the birth-type boundary in the two-mode absorber family, where the beaks- and lips-type classifications meet.

Background

The paper classifies cusp-pair births using the curvature coefficient of the linear-receptance phase-contour locus: positive curvature produces a beaks-type gap-opening reconnection, while negative curvature produces a lips-type isolated-loop birth. Near the type boundary, this curvature coefficient becomes small, so higher-harmonic effects may be comparable to the leading fundamental-harmonic classification.

The authors derive a third-harmonic correction governed by the ratio of the linear receptance at three times the drive frequency to that at the drive frequency. Numerical tests show that the correction can substantially alter the curvature near the boundary, but the boundary displacement itself was not resolved. Thus, it remains unresolved whether the third-harmonic correction changes the location of the transition between the two local birth types.