On the Amplitude of External Perturbation and Chaos via Devil's Staircase — Stability of Attractors

Abstract

We designed a chaotic memristive circuit proposed by Chua and Muthuswamy, and analyzed the behavior of the voltage of the capacitor, electric current in the inductor and the voltage of the memristor by adding an external sinusoidal oscillation of a type γω cos ωt to [Formula: see text], when [Formula: see text] is expressed by y(t)/C, and studied Devil's staircase route to chaos. We compared the frequency of the driving oscillation fs and the frequency of the response fd in the window and assigned W = fs/fd to each window. When capacitor C = 1.0, we observe stable attractors of Farey sequences [Formula: see text], which can be interpreted as hidden attractors, while when C = 1.2, we observe disturbed attractors. Frequency dependent stability of chaotic circuits due to octonions is discussed.