Inducing chaos by resonant perturbations: Theory and experiment

Ying-Cheng Lai, Anil Kandangath, Satish Krishnamoorthy, John A. Gaudet, Alessandro P S De Moura

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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 (US)
Article number214101
JournalPhysical Review Letters
Volume94
Issue number21
DOIs
StatePublished - Jun 3 2005

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Lai, Y-C., Kandangath, A., Krishnamoorthy, S., Gaudet, J. A., & De Moura, A. P. S. (2005). Inducing chaos by resonant perturbations: Theory and experiment. Physical Review Letters, 94(21), [214101]. https://doi.org/10.1103/PhysRevLett.94.214101