Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force

TL;DR

This paper uncovers a new bubbling route to strange nonchaotic attractors in a quasiperiodically forced nonlinear circuit with a nonsinusoidal force, demonstrated through numerical and experimental methods.

Contribution

It introduces the bubbling route as a novel mechanism for SNA formation in a nonsinusoidally forced electronic circuit, supported by comprehensive analysis.

Findings

Bubbles form in quasiperiodic attractors due to square wave forcing.

Bubbles enlarge and become wrinkled as a control parameter varies.

Birth of SNA confirmed by Lyapunov exponents, Poincaré maps, and spectral analysis.

Abstract

We identify a novel route to the birth of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental studies. We find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force. The bubbles then enlarge and get increasingly wrinkled as a function of the control parameter. Finally, the bubbles get extremely wrinkled (while the remaining parts of the strands of the torus remain largely unaffected) resulting in the birth of the SNA which we term as the \emph{bubbling route to SNA}. We characterize and confirm this birth from both experimental and numerical data by maximal Lyapunov exponents and their variance, Poincar\'e maps, Fourier amplitude spectra and spectral distribution function. We also strongly confirm the birth of SNA via the bubbling route by the distribution of the finite-time Lyapunov exponents.