Energy-Dependent Multistability and Offset Boosting in a 5D Generalized Hamiltonian Conservative Hyperchaotic System

A new 5D generalized Hamiltonian conservative system with sine nonlinearity is proposed and investigated. Constructed from a constant antisymmetric structure matrix, the system preserves the generalized Hamiltonian framework while exhibiting enhanced nonlinear dynamics. The derived Hamiltonian function and the zero divergence property confirm that the system is energy conserving and volume preserving. Numerical analyses, including phase portraits, Poincaré sections, bifurcation diagrams, and Lyapunov exponent spectra, show that the system exhibits hyperchaotic behavior and a symmetric Lyapunov spectrum over a relatively wide parameter range. In addition, the system displays energy dependent multistability, coexistence of multiple conservative chaotic orbits under different initial conditions, and offset boosting dependent on initial values. These results enrich the class of high dimensional conservative hyperchaotic systems and provide a useful model for studying complex conservative dynamics within the generalized Hamiltonian framework.