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

We recently analyzed the voltage of the memristic circuit proposed by Muthuswamy and Chua by adding an external sinusoidal oscillation $γω\cosωt$ 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 $ω\simeq 0.5$, we observed a mode of $f_d=1, f_s=2$ at $ω\simeq 1.15$ 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 $ω\simeq 0.85$ 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 $C=1.2$