TY - JOUR
T1 - Inducing chaos in electronic circuits by resonant perturbations
AU - Kandangath, Anil
AU - Krishnamoorthy, Satish
AU - Lai, Ying-Cheng
AU - Gaudet, John A.
N1 - Funding Information:
Manuscript received June 16, 2005; revised September 30, 2006. This work was supported by AFOSR under Grant. F49620-03-1-0290 and Grant FA9550-06-1-0024. This paper was recommended by Associate Editor Y. Nishio.
PY - 2007/5
Y1 - 2007/5
N2 - 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.
AB - 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.
KW - Duffing oscillator
KW - Inducing chaos
KW - Phase-locked loop (PLL)
KW - Resonant perturbations
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U2 - 10.1109/TCSI.2007.893510
DO - 10.1109/TCSI.2007.893510
M3 - Article
AN - SCOPUS:34249077389
SN - 1057-7122
VL - 54
SP - 1109
EP - 1119
JO - IEEE Transactions on Circuits and Systems I: Regular Papers
JF - IEEE Transactions on Circuits and Systems I: Regular Papers
IS - 5
ER -