Twin 5D-Cyclic Symmetric Conservative Hyperchaotic Systems with Sine and Cosine Nonlinearities

Higher-dimensional conservative hyperchaotic systems have recently become a prominent research focus in chaos theory. Based on cyclic symmetry theory, this paper constructs two novel 5D-conservative hyperchaotic systems with distinct characteristics. Employing exclusively sine and cosine functions as their respective nonlinear terms, they are designated as the Sine-type system and the Cosine-type system. Dynamical analyses demonstrate that both systems maintain phase volume conservation, indicating the absence of classical dissipative attractors. Regarding symmetry, both systems exhibit cyclic permutation symmetry; additionally, owing to the inherent odd-symmetric nature of the sine function, the Sine-type system also displays odd symmetry with respect to the origin. Furthermore, driven by periodic nonlinearities, both systems possess infinitely many coexisting conservative chaotic orbits, involving both homogeneous and heterogeneous extreme multistability. Finally, hardware experiments conducted on a DSP platform successfully verify the physical realizability of the Cosine-type system.