Stretching Folding Twisting in the Driven Damped Duffing Device

  • Hernán G. Solari
  • Xin-Jun Hou
  • R. Gilmore
Part of the NATO ASI Series book series (NSSB, volume 208)

Abstract

The results presented here represent another step in our attempt to provide a topological understanding of the behavior of nonlinear dynamical systems. The conditions under which “bifurcation bubbles” exist for a dynamical system has always been a mystery. They occur, for example, in the driven Duffing oscillator. We began by computing the Relative Rotation Rates for the periodic orbits of the Duffing oscillator in order to determine the systematics of “bifurcation bubbles.” The systematics which we have discovered have led to an increased understanding of the mechanics responsible for the bifurcation phenomena seen in driven nonlinear oscillators. In particular, these phenomena can be classified as local bifurcation phenomena and global bifurcation phenomena in a natural way.

Keywords

Periodic Orbit Stable Node Local Bifurcation Duffing Oscillator Bifurcation Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H. G. Solari and R. Gilmore, Phys. Rev. A37, 3096 (1988).MathSciNetCrossRefGoogle Scholar
  2. 2.
    H. G. Solari and R. Gilmore, Phys. Rev. A38, 1566 (1988).MathSciNetGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Hernán G. Solari
    • 1
  • Xin-Jun Hou
    • 1
  • R. Gilmore
    • 1
  1. 1.Department of Physics and Atmospheric ScienceDrexel UniversityPhiladelphiaUSA

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