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.