Nonlinear Dynamics

, Volume 78, Issue 1, pp 317–327 | Cite as

Chaos control in a pendulum system with excitations and phase shift

Original Paper


Melnikov methods are used for suppressing homoclinic and heteroclinic chaos of a pendulum system with a phase shift and excitations. This method is based on the addition of adjustable amplitude and phase-difference of parametric excitation. Theoretically, we give the criteria of suppression of homoclinic and heteroclinic chaos, respectively. Numerical simulations are given to illustrate the effect of the chaos control in this system. Moreover, we calculate the maximum Lyapunov exponents (LEs) in parameter plane, and study how to vary the maximum LE when the parametric frequency varies.


Pendulum equation Phase shift Bifurcation Chaos control Melnikov methods 



The authors would like to thank the reviewers for their helpful comments and suggestions. This work is supported by the National Natural Science Foundation of China (No. 11071066 and No. 11171206).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceHunan University of Science and TechnologyXiangtan People’s Republic of China
  2. 2.College of Mathematics and Computer Science , Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China)Hunan Normal UniversityChangsha People’s Republic of China
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing People’s Republic of China

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