Resumen
The results of detection of periodic signals using the chaos theory based on discrete processing of the Duffing attractor in the Poincare section were considered.A chaotic Duffing system characterized by high sensitivity to periodic signals and a possibility of implementation by means of a relatively simple circuit was chosen for the study.Response of the Duffing system to the periodic influence was analyzed. It was shown that when amplitude of periodic components of the input signal grows at a frequency of driving oscillations, there is a shift of the phase trajectory along the Poincare section which is characterized by fractal geometry. Types of the Duffing attractor changes that result from the influence of a periodic input signal were determined. Control regions for recording types of the phase trajectory dynamics were identified in the phase plane formed by the output signal and its derivative. In accordance with the characteristics of the obtained phase trajectories, a truth table was constructed. It enables estimation of influence of the periodic component with a sufficiently large time sampling increment which is important for ensuring speed of the signal processing devices. Transforms were obtained that describe the process of detecting periodic signals by discrete processing of the Duffing attractor in the Poincare section.Based on the formulated transforms and the truth table, a block diagram of a device for detecting periodic signals in noise was proposed. The proposed device can be used as an input unit to implement the Duffing system based on an analog electric circuit.Values of discrete estimates of amplitude of the periodic component of the input signal according to the shift of the phase trajectory of the Duffing system with respect to the attractor in the Poincare section were obtained. According to the modeling results, the proposed circuit makes it possible to detect periodic signals at low values of the signal-to-noise ratio.