Phase-Locking and Bifurcations of the Sinusoidally-Driven Double Scroll Circuit

Abstract

The dynamic alterations of an electronic circuit in a chaotic regime, described by the Double Scroll attractor, subjected to sinusoidal perturbation are numerically investigated. Parameter diagrams of the circuit phase-locking oscillations in terms of the driving amplitude and frequency are computed. These diagrams have highly interleaved and complex structures, part of them Cantor-like fractals. However, a Cantor-like fractal structure is also observed. In addition, the power spectrum analysis is used to find and characterize three ways of phase-locking the Double Scroll circuit, and to determine how this process depends on the driving parameters. Furthermore, the dynamics of bifurcation phenomena, as chaotic attractor entrainment, Arnold's tongues, coexistence of attractors, and hysteresis are identified in the parameter space.