# The Analysis of Periodic Signal Detection Method Based on Duffing System Chaotic Dynamics

## DOI:

https://doi.org/10.20535/RADAP.2018.74.5-10## Keywords:

weak signal detection, chaotic systems, signal-to-noise ratio, phase portrait## Abstract

This article presents the analysis of periodic signal detection method based on Duffing system sensitivity to weak influences.The described signal detection method is developed with using of Duffing system that oscillates in chaotic state, without transitions to periodic state. The main advantage of such method is the absence of periodic oscillation modes with low sensitivity.

The divergence of Duffing system phase trajectories is investigated with influences of different periodic signals under low signal-to-noise ratio values. The estimation of phase trajectories divergence is performed with using of numeric integration.

The signal detection method is analyzed with different forms of input signal: sinusoidal, square, triangle. The analysis shows that a reliable detection of periodic signal can be performed for any of the three presented forms of signal with repeating frequency near the frequency of the driving signal.

The obtained results show wide capabilities of Duffing system applications for detection of weak periodic signals.

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Copyright (c) 2018 V. V. Martynyuk, Ye. V. Havrylko, J. M. Boiko, M. V. Fedula

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