Weak Signal Detection Application Based on Incommensurate Fractional-Order Duffing System

Abstract

The Duffing Chaos System can detect weak signals that are obscured by Gaussian noise because it is sensitive to specific signal functions and can withstand noise. In this paper, we investigate the use of intermittent chaotic phenomena in fractional-order incommensurate Duffing chaotic systems for weak signal detection. This new intermittent chaotic state has not appeared in integer-order Duffing systems before, so this phenomenon reflects the superiority of fractional-order Duffing systems. We start by giving the incommensurate fractional-order Duffing system’s weak signal detection model. Then design a time series-based judgment method that successfully separates chaotic, intermittent chaotic, and limit cycle states. Finally, the intermittent chaotic of fractional-order detection system is used to determine the amplitude and frequency of the weak signals to calculate the detection performance. The results show that the weak signal can be detected at a maximum signal-to-noise ratio of \(-\)13.26 dB for single-detection oscillator amplitude detection. When detecting the frequency, a single-detection oscillator can detect the frequency range of 1050 rad/s, proving that the fractional-order chaos detection system is better than the integer-order chaos detection system.