Acta Mechanica Sinica

, Volume 12, Issue 3, pp 281–288 | Cite as

Controlling erosion of safe basin in nonlinear parametrically excited systems

  • Xu Jian
  • Lu Qishao
  • Huang Kelei


This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation amplitude are used to observe the variation of the extent and the rate of the erosion in safe basins. It is evident that the appearance of fractal basin boundaries heralds the onset of the losing of structural integrity. The minimum value of control parameter to prevent the basin from erosion is given along with the excitation amplitude varying. The results show the time-dependence of excitation amplitude can be used to control the extent and the rate of the erosion and delay the first occurrence of heteroclinic tangency.

Key Words

excited system safe-basin erosion nonlinear dynamics control fractal 


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Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1996

Authors and Affiliations

  • Xu Jian
    • 1
  • Lu Qishao
    • 1
  • Huang Kelei
    • 1
  1. 1.Department of Applied Mathematics and PhysicsBeijing University of Aeronautics and AstronauticsBeijingChina

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