Analysis and image encryption of memristive chaotic system with coexistence bubble

In recent years, the phenomenon of multistability has attracted wide attention. In this paper, a memristive chaotic system with extreme multistability is constructed by using a memristor. The dynamic behavior of the system is analyzed by Poincaré mapping, a time series diagram, and a bifurcation diagram. The results show that the new system has several significant characteristics. First, the new system has a constant Lyapunov exponent, transient chaos and one complete Feigenbaum tree. Second, the system has the phenomenon of bifurcation map shifts that depend on the initial conditions. In addition, we find periodic bursting oscillations, chaotic bursting oscillations, and the transition of chaotic bursting oscillations to periodic bursting oscillations. In particular, when the system parameters take different discrete values, the system generates a bubble phenomenon that varies with the initial conditions, and this bubble can be shifted with the initial values, which has rarely been seen in the previous literature. The implementation by field-programmable gate array (FPGA) and analog circuit simulation show close alignment with the MATLAB numerical simulation results, validating the system’s realizability. Additionally, the image encryption algorithm integrating DNA-based encoding and chaotic systems further demonstrates its practical applicability.