Inducing chaos by resonant perturbations : Theory and experiment

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-vary...

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Bibliographic Details
Published in:Physical review letters 2005-06, Vol.94 (21), p.214101.1-214101.4, Article 214101
Main Authors: LAI, Ying-Cheng, KANDANGATH, Anil, KRISHNAMOORTHY, Satish, GAUDET, John A, DE MOURA, Alessandro P. S
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.94.214101