Multilayered bubbling route to SNA in a quasiperiodically forced electronic circuit with experimental and analytical confirmation

A new route to strange nonchaotic attractor (SNA), known as multilayered bubble route to SNA, has been identified in a quasiperiodically forced series LCR circuit with a simple nonlinear element. Upon increasing the system control parameter, the stable orbits of the torus become unstable, which induces formation of bubbles in the neighborhood of the resonating region of the torus. We have observed three tori with three smooth branches in the Poincaré map which gradually loose their smoothness and ultimately approach bubble formation, and then approach fractal behavior via SNAs before the onset of chaos. The bubbles gradually enlarge and subsequently another three layers of bubbles are formed as a function of the control parameter. The layers get increasingly wrinkled as a function of the control parameter, resulting in the creation of SNAs which are characterized by Poincaré maps. The multilayered bubble route to SNA is then confirmed by experimental Poincaré maps and explicit analytical solution is developed to further confirm it. Numerically observed bubbling route is characterized qualitatively in terms of phase portraits, power spectrum and further characterized quantitatively, by singular-continuous spectrum analysis, phase sensitivity measure, distribution of finite time Lyapunov exponents, largest Lyapunov exponent and its variance.