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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Influence of Systematic Coupling Stiffness Parameter on Coupling Duffing System Lag Self-synchronization Characteristic

Journal of Applied Nonlinear Dynamics 4(3) (2015) 229--237 | DOI:10.5890/JAND.2015.09.003

Zhao-Hui Ren$^{1}$, Yu-Hang Xu$^{1}$, Yan-Long Han$^{2}$, Nan Zhang$^{1}$, Bang-Chun Wen$^{1}$

$^{1}$ School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110004, China

$^{2}$ Department of Mechanical Engineering, Chengde Petroleum College, Chengde 067000, China

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Self-synchronization, compound synchronization and intelligent control synchronization widely exist in the mechanical system engineering, while lag self-synchronization movement is a special form of cooperation movement. Based on coupling Duffing system, this paper studies lag self-synchronization problem, analyses general change law of the system co-rotating synchronization frequency, antisynchronization frequency and lag phase angle by analytic analysis and numerical quantitative analysis, studies coupling parameter influences on systematic lag self-synchronization, and analyses the cause of lag self-synchronization. The results show that the root cause of lag self-synchronization is systematic stiffness namely systematic natural characteristic; that co-rotating synchronization vibration frequency and phase difference depend on coupling stiffness parameter; and that frequency and phase difference of anti-synchronization vibration are independent of coupling stiffness parameter; and when coupling stiffness parameter is larger, phase difference of two oscillators in the two kinds of synchronization is nonzero constant value.


The authors gratefully acknowledge the financial support provided by Natural Science Foundation of China (No. 51475084).


  1. [1]  Liu, S.Y., Han, Q.K. andWen, B.C. (2001), Dynamic characteristics of vibrating cone crusher with compound synchronization considering materia's activity, Chinese Journal of Mechanical Engineering, 37, 87-89.
  2. [2]  Fan, J., Wen, B.C. (1994), Reverse rotary double vibrator vibration machine synchronous control theory research, Journal Of Vibration Engineering, 7, 281-288.
  3. [3]  Rosenblum, M.G., Pikovsky,A.S. and Kurths, J. (1997), From phase lag synchronization in coupled oscillators, Physical Review Letters, 78, 4193-4196.
  4. [4]  Pikovsky, A. S.and Osipov, G. R., et al (1997), Phase synchronization of chaotic oscillators, Physical Review Letters, 79, 47-50.
  5. [5]  Kocarev, L. and Parlitz, U. (1996), Generalized Synchronization, Predictability, and Equivalence of Unidirectionally Coupled Dynamical Systems, Physical Review Letters, 76, 1816-1819.
  6. [6]  Parlitz, U.and Junge, L. (1997), Subharmonic entrainment of unstable period orbits and generalized synchronization, Physical Review Letters, 79, 3158-3161.
  7. [7]  Lu, J.F. (2008), Communications in Nonlinear Science and Numerical Simulation, 13, 1851-1859.
  8. [8]  Li, D.M., Wang, Z.D., Zhou, J., Fang, J.A. and Ni, J.J. (2008), A note on chaotic synchronization of timedelay secure communication systems, Chaos, Solitons & Fractals, 38, 1217-1224.
  9. [9]  Njah, A.N. and Vincent, U.E. (2008), Chaos synchronization between single and double wells Duffing-Van der Pol oscillators using active control, Chaos, Solitons & Fractals, 37, 1356-1361.