Inducing chaos in electronic circuits by resonant perturbations

Anil Kandangath, Satish Krishnamoorthy, Ying-Cheng Lai, John A. Gaudet

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We propose a scheme to induce chaotic attractors in electronic circuits. The applications that we are interested in stipulate the following three constraints: 1) the circuit operates in a stable periodic regime far away from chaotic behavior; 2) no parameters or state variables of the circuit are directly accessible to adjustment and 3) the circuit equations are unknown and the only available information is a time series (or a signal) measured from the circuit. Under these conditions, a viable approach to chaos induction is to use external excitations such as a microwave signal, assuming that a proper coupling mechanism exists which allows the circuit to be perturbed by the excitation. The question we address in this paper is how to choose the waveform of the excitation to ensure that sustained chaos (chaotic attractor) can be generated in the circuit. We show that weak resonant perturbations with time-varying frequency and phase are generally able to drive the circuit into a hierarchy of nonlinear resonant states and eventually into chaos. We develop a theory to explain this phenomenon, provide numerical support, and demonstrate the feasibility of the method by laboratory experiments. In particular, our experimental system consists of a Duffing-type of nonlinear electronic oscillator driven by a phase-locked loop (PLL) circuit. The PLL can track the frequency and phase evolution of the target Duffing circuit and deliver resonant perturbations to generate robust chaotic attractors.

Original languageEnglish (US)
Pages (from-to)1109-1119
Number of pages11
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Volume54
Issue number5
DOIs
StatePublished - May 2007

Fingerprint

Chaos theory
Networks (circuits)
Phase locked loops
Time series
Microwaves

Keywords

  • Duffing oscillator
  • Inducing chaos
  • Phase-locked loop (PLL)
  • Resonant perturbations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Inducing chaos in electronic circuits by resonant perturbations. / Kandangath, Anil; Krishnamoorthy, Satish; Lai, Ying-Cheng; Gaudet, John A.

In: IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 54, No. 5, 05.2007, p. 1109-1119.

Research output: Contribution to journalArticle

Kandangath, Anil ; Krishnamoorthy, Satish ; Lai, Ying-Cheng ; Gaudet, John A. / Inducing chaos in electronic circuits by resonant perturbations. In: IEEE Transactions on Circuits and Systems I: Regular Papers. 2007 ; Vol. 54, No. 5. pp. 1109-1119.
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