A memristive chaotic system and its application in weak signal detection

In this paper, a novel four-dimensional memristive chaotic system is constructed by incorporating a memristor model into a three-dimensional chaotic system. Through the analysis of the Lyapunov exponent, bifurcation diagram, and Poincaré cross-section of the system, it has been observed that the system is capable of exhibiting a stable chaotic state, as well as complex dynamic behaviors, such as attractor coexistence, transient chaos, and offset boosting. To validate the actual existence of the system, a real circuit has been built based on Multisim simulation, and the numerical simulation results, along with the actual simulation results, are in agreement, thereby confirming the practical feasibility of the circuit. To achieve weak signal detection, a backstepping synchronization controller has been designed, which can detect the frequency and amplitude of unknown signals. It is obvious that this method does not require the determination of the critical threshold. Instead of, it relies on the system being in a chaotic state. The proposed detection method provides a new perspective for weak signal detection.