A new discrete chaotic mapping with unique bifurcation and periodically varying extreme multistability features and its synchronization application

Discrete chaotic systems are considered simpler for computer implementation and large-scale simulation compared to continuous chaotic systems, as the need for solving complex differential equations is avoided. In this paper, a three-dimensional (3D) discrete chaotic map is proposed, which is derived from a continuous system through discretization. The effects of various parameters on the system are analyzed through parameter bifurcations and iterative sequences of state variables. In order to explore the dynamical behaviors of the system more thoroughly, extensive numerical simulations are conducted by adjusting the initial values and parameters. Notably, boosting bifurcations and unique symmetric bifurcations, influenced by the initial values, are observed. Additionally, in contrast to previous studies on offset boosting, offset boosting is achieved through two distinct pathways in this system. During the exploration of extreme multistability, it is found that the system not only coexists with numerous homogeneous attractors, but also that these attractors exhibit diverse periodic changes as the initial values vary. Finally, the system is verified in hardware and a simple synchronization application is carried out.