The geodynamo as a low-dimensional deterministic system at the edge of chaos

We perform non-linear time series analysis tests on the SINT 2000 paleomagnetic record of the Earth's virtual axial dipole moment for the past 2 Ma, and find evidence of low-dimensional deterministic chaos. We reconstruct the phase space attractor using embedded time delay vectors, and compare the result with reconstructions from time series of a turbulent mean-field dynamo model, which exhibits a similar attractor structure. Considered alongside evidence of 1/f noise and lognormality in the paleomagnetic record, this suggests an important role for multiplicative noise, which may maintain the dynamo at the edge of chaos. In contrast to characterisations of geomagnetic reversals as stochastic processes, this work supports their interpretation as the outcome of a deterministic dynamical system.