Is the Solar Cycle an Example of Deterministic Chaos?

Abstract

Recent developments in nonlinear dynamics make it possible to distinguish between random (stochastic) behaviour and deterministic chaos. Trajectories on a chaotic attractor show sensitive dependence on initial conditions. Solar activity exhibits apparently chaotic behaviour on several different timescales, associated with the eruption of active regions, the 22-year magnetic cycle and modulation at grand minima. Although it has not yet been possible to construct a fully convincing self-consistent model of the nonlinear solar dynamo, qualitative features of the solar cycle are reproduced by simple toy systems, such as that investigated by Weiss, Cattaneo & Jones (1984). This sixth order system shows a sequence of three Hopf bifurcations, so that trajectories in the six-dimensional phase space are attracted to a three-torus. Frequency locking is followed by a period-doubling cascade that leads to chaos. The “ghost attractor” still survives and modulates the cycles in a manner reminiscent of the Maunder minimum. This signature of chaos associated with quasiperiodicity is consistent with modulation of the ¹⁴C record but differs from the envelope of the Elatina cycles, which seem to be quasiperiodic rather than chaotic. The Elatina record does not appear to be consistent with the behaviour of the solar cycle over the last 10,000 years.