A class of 5D Hamiltonian conservative hyperchaotic systems with symmetry and multistability

Conservative chaos systems have been investigated owing to their special advantages. Taking symmetry as a starting point, this study proposes a class of five-dimensional(5D) conservative hyperchaotic systems by constructing a generalized Hamiltonian conservative system. The proposed systems can have different types of coordinate-transformation and time-reversal symmetries. Also, the constructed systems are conservative in both volume and energy. The constructed systems are analyzed, and their conservative and chaotic properties are verified by relevant analysis methods, including the equilibrium points, phase diagram, Lyapunov exponent diagram, bifurcation diagram, and two-parameter Lyapunov exponent diagram. An interesting phenomenon, namely that the proposed systems have multistable features when the initial values are changed, is observed. Furthermore, a detailed multistable characteristic analysis of two systems is performed, and it is found that the two systems have different numbers of coexisting orbits under the same energy. And, this type of system can also exhibit the coexistence of infinite orbits of different energies. Finally, the National Institute of Standards and Technology tests confirmed that the proposed systems can produce sequences with strong pseudo-randomness, and the simulation circuit is built in Multisim software to verify the simulation results of some dynamic characteristics of the system.