Inducing Chaos by Resonant Perturbations: Theory and Experiment

Y C Lai, A Kandangath, S Krishnamoorthy, J A Gaudet, A P S de Moura, Ying-Cheng Lai

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25 Citations (Scopus)

Abstract

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.

Original languageEnglish
Article number214101
Number of pages4
JournalPhysical Review Letters
Volume94
Issue number21
DOIs
Publication statusPublished - 3 Jun 2005

Keywords

  • weak harmonic perturbations
  • phase-locked loop
  • parametric perturbations
  • capture range
  • suppression
  • dynamics
  • maintenance
  • broaden

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    Lai, Y. C., Kandangath, A., Krishnamoorthy, S., Gaudet, J. A., de Moura, A. P. S., & Lai, Y-C. (2005). Inducing Chaos by Resonant Perturbations: Theory and Experiment. Physical Review Letters, 94(21), [214101]. https://doi.org/10.1103/PhysRevLett.94.214101