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We made the chaotic circuit proposed by Chua and the memristic circuitproposed by Muthuswamy and Chua, and analyzed the behavior of the voltage ofthe capacitor, electric current in the inductor and the voltage of thememristor by adding an external sinusoidal oscillation ${\dot y}(t)\simeq {\doti_L}(t)$ of a type $\gamma\omega \cos\omega t$, while the ${\dot x}(t)\simeq{\dot v_C}(t)$ is given by $y(t)/C$, and studied the Devil's staircase route tochaos.  We compared the frequency of the driving oscillation $f_s$ and the frequencyof the response $f_d$ in the window and assigned $W=f_s/f_d$ to each window.When capacitor $C=1.0$, we observe stable attractors of Farey sequences$\displaystyle W=\{\frac{1}{2}, \frac{2}{3},\frac{3}{4},\frac{4}{5}, \cdots,\frac{14}{15},\frac{1}{1}\}$, which can be interpreted as hidden attractors,while when $C=1.2$, we observe unstable attractors.  Possible role of octonions in quantum mechanics and Cartan's supersymmetry isdiscussed.

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