Bubble doubling route to strange nonchaotic attractor in a quasiperiodically forced Chua's circuit

Abstract

We have identified a novel mechanism for the birth of Strange Nonchaotic Attractor (SNA) in a quasiperiodically forced Chua's circuit. In this study the amplitude of one of the external driving forces is considered as the control parameter. By varying this control parameter, we find that bubbles appear in the strands of the torus. These bubbles start to double in number as the control parameter is increased. On increasing the parameter continuously, successive doubling of the bubbles occurs, leading to the birth of SNAs. We call this mechanism as the bubble doubling mechanism. The formation of SNA through this bubble doubling route is confirmed numerically, using Poincar\'e maps, maximal Lyapunov exponent and its variance and the distribution of finite-time Lyapunov exponents. Also a quantitative confirmation of the strange nonchaotic dynamics is carried out with the help of singular continuous spectrum analysis.