Period doubling in magnetospheric convection cycle

A gedanken investigation is performed on magnetospheric complexity. In an attempt to separate complexities due to external (solar wind) and internal (magnetospheric) dynamics, we hold the solar wind condition constant and investigate how the open flux in the magnetosphere changes from one convection cycle to the next. The change of open flux is related to the time integral of the tail electric field. This field, in turn, is proportional to the product of the normal (x) and tangential (z) components of the tail magnetic field. As the magnetosphere evolves, the magnetic components typically vary in opposite directions. We show that this competition leads to a magnetic flux cycle described by the classical logistic equation x(n+1) = r(1 - x(n)) x(n), where x is a linear function of open flux, the much researched route to chaos through period-doubling. The result could provide a possible explanation of the steady magnetospheric convection, sawtooth events, and other observed manifestations of nonlinearity.