Finding the Rikitake's attractors by parameter switching

Abstract: In this paper the attractors synthesis algorithm for a class of dissipative dynamical systems with hyperbolic equilibria, presented in [1], is applied to generate any attractor of the Rikitake system. By switching periodically, or even randomly, the control parameter inside a given set of values, during any finite time interval while the attractor is numerically approximated, any attractor can be generated. Beside the extension of the synthesis algorithm to systems with non-hyperbolic equilibria, we have found for the Rikitake system, a new intriguing transient which, occurring for a long time interval, is difficult to be numerically found due to the known system instability along the x3-axis.