Geomagnetic reversals at the edge of regularity

Geomagnetic field reversals remain as one of the most intriguing problems in geophysics and are regarded as chaotic processes resulting from a dynamo mechanism. In this article we use the polarity scale data of the last 170 Myrs collected from the ocean floor to provide robust evidence for an inverse relationship between the complexity of sequences of consecutive polarity intervals and the respective reversal rate. In particular, the variability of sequences of polarity intervals reaches minimum values in the mid-Jurassic when a maximum reversal rate is found, in the early Cretaceous preceding the Cretaceous Superchron, and twice in the last 20 Myrs. These facts raise the possibility of epochs of high regularity in the geomagnetic field reversals. To shed light on this process, we investigate the transition from regular to chaotic regime in a minimal model for geomagnetic reversals. We show that even in chaotic regimes, the system retains the signature of regular behavior near to transitions. We suggest that geomagnetic reversals have switched between different degrees of irregularity, with a dominant periodicity of approximate to 70 kyrs that results from the occurrence of "ghost" limit cycles (GLCs) or unstable periodic orbits (UPOs) immersed in a chaotic region of phase space.