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 Rikitake two-disk dynamo chaotic system. We also derive new results for the state regulation of the Rikitake two-disk dynamo chaotic system. MATLAB plots have been depicted to illustrate the phase portraits of the Rikitake twodisk dynamo chaotic attractor and the state regulation of the Rikitake two-disk dynamo chaotic system with unknown system parameters via adaptive control method.