A new complex Duffing oscillator used in complex signal detection

In view of the fact that complex signals are often used in the digital processing of certain systems such as digital communication and radar systems, a new complex Duffing equation is proposed. In addition, the dynamical behaviors are analyzed. By calculating the maximal Lyapunov exponent and power spectrum, we prove that the proposed complex differential equation has a chaotic solution or a large-scale periodic one depending on different parameters. Based on the proposed equation, we present a complex chaotic oscillator detection system of the Duffing type. Such a dynamic system is sensitive to the initial conditions and highly immune to complex white Gaussian noise, so it can be used to detect a weak complex signal against a background of strong noise. Results of the Monte-Carlo simulation show that the proposed detection system can effectively detect complex single frequency signals and linear frequency modulation signals with a guaranteed low false alarm rate.