Characterizing the attractors of chaotic systems by a direct measurement method

Abstract

Due to the high sensitivity to internal parameters, the operation of the chaotic systems may couple strongly to the ambient and are apt to detect small variations of external factors that influence the internal ones. We present details of a method and related equipment for analyzing and characterizing the behavior of chaotic systems, suited for assessing changes in the dynamics. The method essentially consists in determining the probability that the trajectory of the chaotic system is located in a specified region of the phase space. The method is based on the measurement of the time intervals spent by the trajectory in the specified phase space interval. The measuring equipment is a high precision time measuring one, based on microcontrollers. We exemplify the method by assessing the dependency of the behavior of a chaotic electronic circuit on the variation of the power supply voltage.

Biomimetic Chaotic Sensor for Moderate Static Magnetic Field

“…Next, we calculated the time average V 1 (t) . This average is a duty cycle factor used to characterize continuous changes in the chaotic attractor with variations in the target signal [16]. The obtained results are presented in Figure 3.…”

“…The attractor of a nonlinear system can consist of parts concentrated in different regions of the phase space, with fast transitions in the dynamic trajectory between these parts. A bistable sensor based on these chaotic dynamics requires neither an external driving signal (as in fluxgate magnetometers [14]) nor noise (as in noise-activated sensors [15]) for its functioning [16]. Its output can be quantified by the spike count rate [17], with spikes defined by times of dynamic trajectory crossings between attractors.…”

Sensors based on nonlinear dynamic systems — A survey

“…Several photoresistors were used [25,29] in the feedback circuit to measure light, see Fig. 11, [30][31][32]. Figure 11.…”

“…The feedback circuit of Sprott's chaotic system with photoresistors, as used in [25,29]. From [30][31][32].…”

“…Examples of visual binary patterns (left, lower corner) and the enclosure of the measuring system; in the thermostated enclosure are the retina, the light source, the tested paterns, and a thermostat circuit. (Based on [30][31][32], device man-made by the second author of [30][31][32], with author's supervision and key ideas).…”