Exploring extreme multistability in cyclic symmetric conservative systems via two distinct methods

In recent years, conservative systems have received increasing attention. However, research on cyclic symmetric conservative systems remains relatively limited. This paper presents two cyclic symmetric conservative systems and explores two methods to explore extreme multistability. Both systems maintain constant volume and zero-sum Lyapunov exponents. The four-dimensional conservative chaotic system, aided by the periodicity of the sine function terms, displays both homogeneous and heterogeneous extreme multistability. For the five-dimensional conservative hyperchaotic system, an improved offset boosting control method is adopted, causing it to exhibit extreme multistability in multiple directions, achieving the effect of hyperchaotic roam. Moreover, using the five-dimensional system as an example, the application of cyclic symmetric conservative systems in data encryption transmission is implemented. Finally, the physical feasibility of the system is verified using circuit simulation software and the DSP platform.