Analysis and observer design for the Bullard and Rikitake dynamos

The Bullard dynamo and the Rikitake system are two well-known non-linear systems, which are used to capture the main aspects of the magnetic field of the Earth, especially those non-linear and chaotic. Aim of this study is two-fold: the review, on the basis of the modern differential geometry, of the dynamical aspects of both systems, and the design, on the basis of the modern geometric control theory, of dynamical algorithms for the estimation of the state variables, which is a challenging problem because of the chaotic behaviour presented by both systems. All the analyses are validated in simulation.