A tri-valued memristive chaotic system with hidden attractors and its image encryption application

This paper presents a chaotic system with hidden attractors by introducing a tri-valued memristor into the Liu chaotic system. The attractors have a rich topology, as shown by the analysis of the phase diagram, Poincaré diagram, Lyapunov exponential spectrum and bifurcation diagram, and we try to summarize the regularity of the system characteristics within a certain range of controllable parameters. We analyzed attractors with strange shapes by setting different parameters, and the multistability and the transient behavior is analyzed, which reflects the high complexity of the system, The complexity characteristics of the system are also analyzed by calculating the SE value and C0 complexity, the corresponding circuit is designed, and the simulation analysis of the system is carried out to verify the physical realizability of the system. Finally, this system is applied to image encryption to analyze its security from a histogram and correlation perspective. These findings provide a reference value for the tri-valued memristor based system for encryption applications. Graphical abstract The left box is descriptions of how to build the system, and the right box is the descriptions of the phenomena produced by the three parameters a,b and h,the middle part is the dynamics analysis, complexity analysis, and circuit design of the system