Figure 1

(a) Stick balanced at the fingertip. (b) Temporal series for $\frac{\Delta z}{l}$ for a 62 cm stick balanced at the fingertip. The data was sampled at 120 Hz. The horizontal line depicts the threshold position at 1.0005 times the mean value. (c) Log-log plot of the power spectrum for the fluctuations in $\frac{\Delta z}{l}$. It is characterized by two power law regimes with exponents close to $-\frac{1}{2}$ (upper line) and $-2.4$ (lower line). (d) Normalized laminar phase probability distribution, $P(\delta t)$. The triangles are calculated from a single realization and the circles represent the mean distribution obtained from 48 realizations. The normalization of the $P(\delta t)$ is done to permit comparison between different realizations. The dashed line represents a power law with exponent $-\frac{3}{2}$.Reuse & Permissions

Figure 2

(a) Stability domain of (1) in the deterministic situation computed as follows: For each pair $(R_0,\tau )$, (1) was integrated using an Euler algorithm with step size $h={10}^{-3}$ an initial condition $\theta (s)=0$ for $s\in [0,-\tau ]$. We assumed that the system escaped whenever $\theta (t)>\frac{\pi }{2}$ for $\frac{t}{h}<2^{23}$; otherwise, we assumed that the parameter pair belonged to the stability domain. The stability boundary determined in this way is expected to approximate the true stability boundary for $t\to \infty$; i.e., the true stability domain is likely smaller than shown. Representative time series for the parameter choices corresponding to the solid symbols in (a) are shown, respectively, from top to bottom, in (b), (c), (d), and (e). Parameter values are indicated on the axis of (a).Reuse & Permissions

Figure 3

Log-log plot of the (a) power spectrum characterized by two power law regimes with exponents close to $-\frac{1}{2}$ (upper line) and $-2.4$ (lower line) and (b) laminar phases distribution for (1) for three different values of the total number of laminar phases, from top to bottom: $3\times {10}^6$, $2\times {10}^6$, and ${10}^6$. Numerical integration was performed using an Euler algorithm with a step size of ${10}^{-3}$. The initial integration time of $50\tau$ was discarded and (1) was further integrated $>{10}^7\tau$ to obtain the data to calculate (a) and (b). Parameter values for the simulations were $\tau =0.07\sec $, $R_0=0.226981$, $\sigma =0.13$, and $\gamma =100$.Reuse & Permissions