IJMNTA  Vol.3 No.3 , July 2014
On Slide Mode Control of Chaotic Rikitake Two-Disk Dynamo—Chaotic Simulations of the Reversals of the Earth’s Magnetic Field

The modern nonlinear theory, bifurcation and chaos theory are used in this paper to analyze the dynamics of the Rikitake two-disk dynamo system. The mathematical model of the Rikitake system consists of three nonlinear differential equations, which found to be the same as the mathematical model of the well-known Lorenz system. The study showed that under certain value of control parameter, the system experiences a chaotic behaviour. The experienced chaotic oscillation may simulate the reversal of the Earth’s magnetic field. The main objective of this paper is to control the chaotic behaviour in Rikitake system. So, a nonlinear controller based on the slide mode control theory is designed. The study showed that the designed controller was so effective in controlling the unstable chaotic oscillations.

Cite this paper: Harb, A. and Ayoub, N. (2014) On Slide Mode Control of Chaotic Rikitake Two-Disk Dynamo—Chaotic Simulations of the Reversals of the Earth’s Magnetic Field. International Journal of Modern Nonlinear Theory and Application, 3, 136-143. doi: 10.4236/ijmnta.2014.33015.

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