Hopf Bifurcations and Degeneracies in Chua ’ S Circuit a Perspective from a Frequency Domain Approach

  title={Hopf Bifurcations and Degeneracies in Chua ’ S Circuit a Perspective from a Frequency Domain Approach},
  author={Jorge L. Moiola and Leon O. Chua},
In the present work explicit formulas for analyzing the birth of limit cycles arising in the Chua’s circuit through a Hopf bifurcation is provided. A local amplitude equation is derived using a frequency domain approach and harmonic balance approximations. Furthermore, the first Lyapunov index used to detect degenerate Hopf bifurcations is derived in terms of the parameters of the nonlinear circuit. A perspective for analyzing other bifurcations using this frequency domain approach is discussed… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 20 references

Bifurcation Phenomena in CSTR Dynamics, PhD thesis, University of Minnesota

  • J. B. Planeaux
  • 1993
Highly Influential
3 Excerpts

Subharmonic resonances in a driven oscillator: Bifurcation structures and transitions to chaos,

  • L JanickiK., W. Szemplinska-Stupnicka
  • European J. Mech. A/Solids
  • 1997

Efficient determination of higher - order periodic solution using nmode harmonic balance

  • M. Golubitsky, W. F. Langford
  • IMA J . Appl . Math .
  • 1996

Eleven small limit cycles in a cubic vector field,

  • H. Zoladek
  • Nonlinearity
  • 1995
2 Excerpts

Symmetry - breaking and firstperioddoubling following a Hopf bifurcation in a three dimensional system

  • D. W. Berns, J. L. Moiola
  • Mech . Res . Commun .
  • 1995

Chua’s circuit: Rigorous results and further problems,

  • L. P. Shil’nikov
  • Int. J. Bifurcation and Chaos
  • 1994
1 Excerpt

1993b] “On periodic orbits and homoclinic bifurcations in Chua’s circuit with a smooth nonlinearity,

  • A. I. Khibnik, D. Roose, L. O. Chua
  • Int. J. Bifurcation and Chaos
  • 1993
3 Excerpts

Bifurcation phenomena in a nonlinear oscillator: Approximate analytical studies versus computer simulation results,

  • W. Szemplinska-Stupnicka, J. Rudowski
  • Physica D66,
  • 1993

Similar Papers

Loading similar papers…