Dynamical analysis of a new memristive map with offset boosting and extreme multistability

In this paper, a memristive circuit is designed based on a charge-controlled memristor, and the Hamilton energy function is obtained from the Helmholtz theorem. The system equation of memristive circuit is discretized by redefining the variables to obtain a three-dimensional memristive map and the corresponding energy function. Then, the effects of parameters and initial values on the memristive map are analyzed using conventional dynamical analysis. There are multiple types of quasi-periodic and chaotic states of the memristive map under different parameters, and the energy evolution of different states is shown. In addition, offset boosting and homogeneous extreme multistability are found in the map, which can be controlled to offset the attractor by changing specific parameters and initial values. The complexity of the chaotic sequence is also analyzed as the parameters and initial values are varied over the chosen range. Finally, the map is implemented on PSIM circuit simulation and digital signal processor (DSP) respectively. This research will provide a reference for secure communication.