A novel three-dimensional chaotic system with double wings and spiral chaos: Applications in ship radiation noise detection

Aiming at the deficiency of a traditional two-dimensional chaotic system in detection performance, a three-dimensional double-wing chaotic system (3DDWCS) with a sine term is proposed and applied to the detection of ship radiated noise (SRN). Firstly, the nonlinear characteristics of 3DDWCS are analyzed in detail, such as bifurcation, Lyapunov exponent and equilibrium point. Secondly, fractional-order calculus is introduced into 3DDWCS, and a fractional-order 3D double-wing chaotic system (FO3DDWCS) is proposed. The critical threshold of FO3DDWCS is determined by the bifurcation diagram and verified by phase trajectory. Thirdly, in the performance analysis experiment, the signal-to-noise ratio (SNR) threshold of FO3DDWCS considering the fractional-order derivative is -124.94 dB, which is obviously superior to the integer-order 3D chaotic system and the improved fractional-order chaotic system based on a Duffing oscillator in noise immunity. It has a good detection effect and realizes the detection of signals under the ultra-low SNR threshold. Finally, a weak signal detection method based on FO3DDWCS is proposed and successfully applied to the detection of multi-line spectral periodic signals, distorted signals, SRN and marine biological signal, which verifies the effectiveness and practicability of the proposed detection method.