Chaos theory has a manifold variety of applications in science and engineering. The frequent and irregular reversals of the earth’s magnetic field has motivated a number of research studies involving electrical currents within the earth’s molten core. One of the first such nonlinear models that exhibited the frequent and irregular reversals of the earth’s magnetic field was Rikitake’s two-disk dynamo system (1958). Rikitake two-disk dynamo system is a chaotic system that predated the pioneering work of Lorenz (1963). In this paper, we describe the dynamic equations and qualitative properties of the Rikitae two-disk dynamo chaotic system. We also derive new results for the global anti-synchronization of the Rikitake two-disk dynamo chaotic systems. MATLAB plots have been depicted to illustrate the phase portraits of the Rikitake two-disk dynamo chaotic attractor and the global anti-synchronization of the Rikitake two-disk dynamo chaotic systems via adaptive control method.