Figure 4

(a) Complexity-entropy diagram for the spontaneously oscillating hair bundle in Fig. (2). For all data sets, “■” and “▲” represent fully sampled and sub-sampled data sets, respectively. Blue and teal colours represent raw hair bundle oscillation data and phase-shuffled surrogate data, respectively. Red represents the time series of a numerical simulation of the normal form equation for the supercritical Hopf bifurcations, driven by noise. Orange represents the corresponding phase-shuffled surrogate data set of this Hopf oscillator. Dark green and light green represent telegraphic noise and the corresponding surrogate data, respectively. “•” corresponds to fractional Brownian motion with Hurst exponent ranging from 0.02 to 0.98. The black curves confine all possible probability distributions. The dashed curve is the half-way point between the upper and lower bounds and serves as an approximate boundary between stochastic and chaotic processes. (b) The Kolmogorov entropy of an oscillatory hair bundle subject to a sinusoidal drive (“”), and transfer entropy from stimulus to hair bundle (“•”). As a control (“○”), transfer entropy from hair bundle to stimulus is also plotted as a function of the stimulus amplitude. Vertical dashed lines delineate approximate regions that correspond to Poincaré maps displaying cloud, ring, and point structures, as illustrated by the schematic diagrams above the graph. Noise floors are indicated by horizontal dashed lines. The noise floor on the K-entropy is estimated by tracking the motion of a passive hair bundle driven by a 10–25 pN sinusoidal stimulus. The noise floor on the transfer entropy is estimated based on bundle oscillations in the absence of a stimulus. Uncertainties in K-entropy are estimated by taking the standard deviation of the residuals from the linear fit of Shannon entropy with time. Uncertainties in transfer entropy are estimated from a bootstrapping technique that incorporates the uncertainties in position measurements.