The design of a four-wing chaotic system and the application of synchronous control in weak signal detection

Abstract

Simple fourth-order autonomous differential equations can exhibit chaotic properties. In this paper, a chaotic system with a four-wing attractor is proposed where the varying number of attractor wings depends not only on the system parameters but also on the initial state of the system. First, the phase diagram, Lyapunov exponential (LE) spectrum, bifurcation diagram, Poincaré section diagram and 0–1 test diagram can verify that the system has more complex dynamic characteristics. Meanwhile, not only is the randomness of the system is verified by complexity analysis, but the multistability of the system, namely, the coexistence attractor, is also simulated. Second, using Multisim to build an analog circuit diagram, the circuit simulation results and numerical simulation results coincide, proving the circuit feasibility of the system. Finally, a suitable controller is designed based on Lyapunov stability theory to realize the synchronization of the drive-response system. On the basis of synchronization, disturbance (measured signal) is added to the response system to transform the signal detection into the synchronization error analysis of the drive-response synchronization system. The frequency of synchronization error is obtained by frequency domain analysis, and the frequency value estimated by the multiple signal classification (MUSIC) algorithm. It is found that the proposed chaotic system has more complex dynamics. The method of synchronization control error combined with spectrum estimation can effectively estimate the frequency of weak signal and provide a large detection threshold for weak signal detection.