arXiv subjects

Tomoyuki Takano

Publications and source records attributed to Tomoyuki Takano.

2 recordsLinked to original sources

arXiv2015

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

We made the chaotic circuit proposed by Chua and the memristic circuit proposed by Muthuswamy and Chua, 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 ${\dot y}(t)\simeq {\dot i_L}(t)$ of a type $γω\cosωt$, while the ${\dot x}(t)\simeq {\dot v_C}(t)$ is given by $y(t)/C$, and studied the Devil's staircase route to chaos. We compared the frequency of the driving oscillation $f_s$ and the frequency of 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 is discussed.

nlin.CD↗

arXiv2014

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 $C=1.2$

nlin.CD↗