Reliability analysis of weak signal detection based on Duffing oscillator

Chaotic system is sensitive to weak signals with the same frequency as the driving force, and is also immune to noise. Ever since Brow first proposed Duffing oscillator being used to detect weak signal^[1], a great deal of research have been done in this field, including selection of the driving threshold value, impact of noise on phase orbit, identification of large-scale periodic state and chaotic state^[2-4] and so on, but a few studies have been done about the effect of initial conditions on detection reliability of the chaotic system. The initial condition of Duffing oscillator selected by some researchers is random and uncertainty. This paper concluded from stimulation results that different initial conditions lead to different transitional process and different immunity to noise, and recommended a proper selection method of initial conditions and input time of weak signals with background noise, which can effectively improve the detection reliability of chaotic system.