Duffing Oscillator Model of Solar Cycles

We propose that the solar cycle variability could be described in the framework of an external quasi-sinusoidal influence on an oscillator with cubic nonlinearity and linear damping (Duffing oscillator). To demonstrate this, we compare the empirical amplitude–frequency dependence with the theoretical one obtained by the Krylov–Bogolyubov averaging method. The empirical data are a composite time series of 2.0 version of sunspot number series, which starts in 1700, and the sunspot group number series by Svalgaard & Schatten, scaled to sunspot number, for 1610–1699 interval. We find that while this interpretation of solar cycle is a mathematical approximation, it explains several properties of solar cycle variability.