A Parameter-Space Analysis of the Rikitake System

We investigate analytically and numerically the dynamics of the Rikitake system. The Routh–Hurwitz criterion is used to study the stability of the equilibrium points of the differential equation system model, as functions of two parameters. The dynamics of the model are numerically studied using diagrams that associate colors to the largest Lyapunov exponent value, in two-dimensional parameter spaces. Additionally, phase-space plots and bifurcation diagrams are used to distinguish periodic and chaotic attractors.