Extreme multistability and its realization in a simple 6D hyperchaotic system with only sinusoidal nonlinearity

Since high-dimensional hyperchaotic systems typically require two or more nonlinear terms to exhibit rich dynamical behaviors, this paper proposes for the first time a simple six-dimensional hyperchaotic system that simultaneously possesses complex phenomena. The system contains only a single sinusoidal nonlinearity involving only one state variable. Although the system has only one nonlinear term, analyses via Lyapunov exponents and bifurcation diagrams demonstrate that it possesses an ultra-wide hyperchaotic range, and varying the system parameters can alter the attractor topology. Compared with related research works, the proposed system exhibits extreme multistability, transient phenomena, transient chaos, and offset boosting along six dimensions. The simultaneous emergence of these complex phenomena is reported here for the first time among existing systems with a single nonlinear term. The complexity and randomness of the system are subsequently analyzed. Finally, a dual-hardware implementation of the system is carried out through a Field-Programmable Gate Array (FPGA) and a Digital Signal Processor (DSP). Experimental results verify the correctness of the theoretical analysis, providing support for the application of this hyperchaotic system in fields such as secure communication.