For multi-degree-of-freedom dynamical systems, a novel control method was proposed to realize synchronization and anti-synchronization of chaos between the original and derived systems. The presented method was proved theoretically and realized by linear coupling of velocity. Furthermore, for any coupling coefficient larger than the critical value, the two systems can continue synchronization and anti-synchronization by the coupling method. This means that the synchronization and anti-synchronization can be kept within a wide range of coupling parameters. The simulation results for Duffing and Mathieu systems proved that the proposed method was correct and effective.
ChangS (2010) Synchronization and controlling chaos in a permanent magnet synchronous motor. Journal of Vibration and Control16: 1881–1894.
2.
ChenHH (2007) Adaptive synchronization of chaotic systems via linear balanced feedback control. Journal of Sound and Vibration306: 865–876.
3.
ChuYDZhangGJLiXFChangYXLuoGW (2008) Chaos and chaos synchronization for a non-autonomous rotational machine systems. Nonlinear Analysis – Real World Applications9: 1378–1393.
4.
GeZMLeeC (2005) Anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor. Journal of Sound and Vibration282: 635–648.
5.
MahmoudGAhmedM (2010) Modified projective synchronization and control of complex Chen and Lü systems. Journal of Vibration and Control17: 1184–1194.
6.
NjahAN (2010) Synchronization via active control of parametrically and externally excited Φ6 Van der Pol and Duffing oscillators and application to secure communications. Journal of Vibration and Control17: 493–504.
7.
PadmanabanEHensEDanaSK (2011) Engineering synchronization of chaotic oscillators using controller based coupling design. Chaos21: 013110–013110.
8.
PecoraLCarrollTL (1990) Synchronization in chaotic systems. Physical Review Letters64: 821–824.
9.
RoopaeiMJahromiMZJafariS (2009) Adaptive gain fuzzy sliding mode control for the synchronization of nonlinear chaotic gyros. Chaos19: 013125–013125.
10.
SorrentinoF (2010) The stability of adaptive synchronization of chaotic systems. Chaos20: 013103–013103.
11.
StefańskiAKapitaniakT (2003) Synchronization of two chaotic oscillators via a negative feedback mechanism. International Journal of Solids and Structures40: 5175–5185.
12.
WangXWangJ (2007) Synchronization and anti-synchronization of chaotic systems based on linear separation and applications in security communication. Modern Physics Letters B21: 1545–1553.
13.
WuXCaiJWangM (2007) Robust synchronization of chaotic horizontal platform systems with phase difference. Journal of Sound and Vibration305: 481–491.
