Nonlinear resonance in an overdamped Duffing oscillator as a model of paleoclimate oscillations

The cause of the dominant 100-kyr cycles in Earth's paleoclimate in the last 800 000 years has since long been debated. We analyze geological temperature proxy data and retrieve an anharmonic potential from time series data. The obtained potential has bistable features but has significant differences compared to the quartic potentials derived from theoretical energy-based models. Subsequently, we demonstrate the existence of vibrational resonance (VR) and nonlinear resonance phenomena at the combination tones of the driving frequencies in a simple bistable potential without self-sustained oscillations. We find that periodic forcing by the obliquity and frequencies similar to those of the precession cycle can generate output dominated by 100-kyr cycles, thereby offering a mechanism for explaining the observations in geological data. While previous studies of VR have assumed one periodic driver to have a frequency much higher than the other, we show that for a range of amplitudes, both phenomena can occur at the orbital cycle frequencies. We find that the nonlinear resonance phenomenon is more robust to noise than VR between eccentricity and obliquity and emerges within a much larger range of amplitudes of forcing. Finally, we conclude that it is conceivable that nonlinear resonance between obliquity and precession might explain the spectral frequencies observed in the late Pleistocene.