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

TL;DR

This paper introduces a new bubble doubling mechanism for the formation of strange nonchaotic attractors in a quasiperiodically forced Chua's circuit, confirmed through numerical analysis including Lyapunov exponents and spectral methods.

Contribution

The study reveals a novel bubble doubling route to SNA in a Chua's circuit, expanding understanding of attractor formation mechanisms in nonlinear dynamical systems.

Findings

Bubbles in the torus strands double with increasing control parameter.

Successive bubble doubling leads to the emergence of SNA.

Numerical methods confirm the strange nonchaotic nature of the attractors.

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.