Modeling numerically the Rikitake's attractors by parameter switching

In this paper the attractors synthesis algorithm for a class of dissipative dynamical systems with hyperbolic equilibria, presented in [1], is applied to model numerically any attractor of the Rikitake system. By switching periodically, or even randomly, the control parameter inside a given set of values, while the underlying initial value problem is numerically integrated, any attractor can be obtained. 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.