Hysteresis in a Solar Activity Cycle

We analyze in situ measurements of solar wind velocity obtained by the Advanced Composition Explorer (ACE) spacecraft during the solar activity cycle 23. We calculated a robust complexity measure, the permutation entropy (S) of the solar wind time series at different phases of a solar activity cycle. The permutation entropy measure is first tested on the known dynamical data, before its application to the solar wind time series. It is observed that the complexity of solar wind velocity fluctuations at 1 AU shows the phenomenon of hysteresis while following the ascending and descending phases of the activity cycle. This indicates the presence of multistability in the dynamics governing the solar wind velocity over a solar activity cycle.