On the Amplitude of External Perurbation and Chaos via Devil's Staircasein Muthuswamy-Chua System

Abstract

We recently analyzed the voltage of the memristic circuit proposed by Muthuswamy and Chua by adding an external sinusoidal oscillation $\gamma \omega \cos \omega t$ to the $\dot{y}(t)\simeq {\dot{i}}_L(t)$, when the $\dot{x}(t)\simeq {\dot{v}}_C(t)$ is given by $y(t)/C$. When $f_s<f_d$ we have observed that the Hölder exponent of the system with $C=1$ is larger than 1, and that of the system with $C=1.2$ is less than 1. The latter system is unstable, and the route to chaos via the devil's staircase is observed. Above the mode of $f_d=1,f_s=1$ observed at $\omega \simeq 0.5$, we observed a mode of $f_d=1,f_s=2$ at $\omega \simeq 1.15$ and $\simeq 1.05$, in the case of $C=1$ and 1.2, respectively, and a mode of $f_d=2,f_s=3$ at $\omega \simeq 0.85$ and $\simeq 0.78$, in the case of $C=1$ and 1.2, respectively. At high frequency of $f_s$, there is no qualitative difference in the stability of the oscillation for $C=1$ and $C=1.2$

14 pages, 22 figures, added some corrections to texts

Cited by in corpus (1)

• On the amplitude of External Perturbation and the Chaos via Devil's Staircase -Stability of Attractors -