Evidence for chaotic behaviour in pulsar spin-down rates

We present evidence for chaotic dynamics within the spin-down rates of 17 pulsars originally presented by Lyne et al. Using techniques that allow us to re-sample the original measurements without losing structural information, we have searched for evidence of a strange attractor in the time series of frequency derivatives for each of the 17 pulsars. We demonstrate the effectiveness of our methods by applying them to a component of the Lorenz and R\"ossler attractors that were sampled with similar cadence to the pulsar time series. Our measurements of correlation dimension and Lyapunov exponent show that the underlying behaviour appears to be driven by a strange attractor with approximately three governing non-linear differential equations. This is particularly apparent in the case of PSR B1828$-$11 where a correlation dimension of 2.06\pm0.03 and a Lyapunov exponent of $(4.0\pm0.3)\times10^{-4}$ inverse days were measured. These results provide an additional diagnostic for testing future models of this behaviour.