Memristor-based chaotic system with abundant dynamical behaviors and its application

The memristor is a controllable nonlinear element that can easily generate chaotic signals. Currently, most researchers focus on the nonlinear properties of memristors, while the ability of memristor to control and adjust chaotic systems has rarely been addressed. Therefore, we design a memristor-based chaotic system to produce the upper-lower attractors by changing the polarity of the memristor. Dynamics phenomena, such as multi-stability, transient phenomena, sustained chaos, bi-stability and intermittent chaos, are observed in the system. Several fundamental dynamical behaviors, including the stability of equilibria, symmetry, and dissipation, are investigated. To prove the physical existence of the system, we give the PSPICE circuit simulation and the MCU (microcontroller unit) hardware implementation. Additionally, the theory of stochastic differential equations is applied to demonstrate the immunity of the system to zero-mean Gaussian noise. Based on the designed recursive back-stepping controller and the proposed chaotic system, we present a new method to detect weak multi-frequency signals embedded in Gaussian noise. Experimental results demonstrate that the proposed method is able to detect each frequency of a multi-frequency weakly periodic signal submerged in a Gaussian noise background, which is important for promoting the engineering application of the memristor.