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Chaos, chaos control and synchronization of a gyrostat system. (English) Zbl 1237.70019

Summary: The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.

MSC:

70E05 Motion of the gyroscope
34H10 Chaos control for problems involving ordinary differential equations
70-08 Computational methods for problems pertaining to mechanics of particles and systems
93C10 Nonlinear systems in control theory
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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