Modeling a 5D Hamiltonian conservative hyperchaotic oscillator with complicated dynamics

Abstract Based on the 3D Euler equation, 5D generalized Euler equations are realized by introducing three coupling parameters and combining three subbodies with two same axes, whose Casimir energy and Hamiltonian are both conservative. By violating the Casimir energy conservation, a 5D Hamiltonian hyperchaotic oscillator is postulated. Through nonlinear analysis methods, it is found that the 5D Hamiltonian conservative hyperchaotic system possesses complicated dynamic behaviors, such as a wide constant range, hidden chaotic orbit, bursting oscillation, transient bursting, and multi-orbit coexistence. Then, the National Institute of Standards and Technology (NIST) statistical test suite is employed to evaluate the randomness quality of the pseudo-random sequences generated by the system, indicating their potential suitability for chaos-based cryptographic applications. Finally, the physical feasibility of the oscillator is validated through both analog circuit simulation and STM32-based hardware implementation.