Multiperiodicity, chaos, and intermittency in a reduced model of the solar cycle

In a recent paper, Durney (2000) has discussed a physically plausible procedure whereby the dynamo equations describing magnetic field regeneration in Babcock-Leighton models of the solar cycle can be reduced to a one-dimensional iterative map. This procedure is used here to investigate the behavior of various dynamo-inspired maps. Durney's explanation of the so-called odd-even effect in sunspot cycle peak amplitudes, which he ascribed to a period-2 limit cycle, is found to be robust with respect the choice of nonlinearity defining the map, and to the action of strong stochastic forcing. In fact, even maps without limit cycles are found to show a strong odd-even signal in the presence of forcing. Some of the stochastically forced maps are found to exhibit a form of on-off intermittency, with periods of activity separated by quiescent phases of low cycle amplitudes. In one such map, a strong odd-even signal is found to be a good precursor to the transition from bursting to quiescent behavior.