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Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping. (English) Zbl 1237.70094
Summary: The dynamic behavior of a symmetric gyro with linear-plus-cubic damping, which is subjected to a harmonic excitation, is studied in this paper. The Liapunov direct method has been used to obtain the sufficient conditions of the stability of the equilibrium points of the system. By applying numerical results, time history, phase diagrams, Poincaré maps, Liapunov exponents and Liapunov dimensions are presented to observe periodic and chaotic motions. Besides, several control methods, the delayed feedback control, the addition of constant motor torque, the addition of period force, and adaptive control algorithm (ACA), have been used to control chaos effectively. Finally, attention is shifted to the synchronization of chaos in the two identical chaotic motions of symmetric gyros. The results show that one can make two identical chaotic systems to synchronize through applying four different kinds of one-way coupling. Furthermore, the synchronization time is also examined.

MSC:
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
70Q05 Control of mechanical systems
34H10 Chaos control for problems involving ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D99 Stability theory for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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