Phenomenological Models of the 11-Year Solar Periodicity and Its Empirical Rules

In this paper, we describe and analyze a method for constructing phenomenological models of the 11-year solar cycle based on a nonlinear oscillator equation with damping and external noise. It is demonstrated that such models can reproduce the known empirical relationships between the parameters of the cycles: the Waldmeier and Chernosky rules. The Gnevyshev-Ohl rule (understood in its original meaning as “correlation”) proved to be the most difficult to reproduce in a model. In this paper, we discuss possible ways to overcome this difficulty. In edition, the constructed models can reproduce another feature seen in observational data — long periods of reduced global activity or “grand minima”.