Construction of a family of 5D Hamiltonian conservative hyperchaotic systems with multistability

Compared with the dissipative chaotic system, the conservative chaotic system is more suitable for engineering applications because of its phase volume conservation, no attractor and better ergodicity. In order to enrich the research of conservative chaos theory, this paper introduces a universal method to construct 5D Hamiltonian conservative hyperchaotic systems. Four 5D sub-Euler equations are derived, and ten 5D Euler equations are obtained by combining them with the existing sub-Euler equations. Taking one of the Euler equations as an example, the specific process of constructing a 5D Hamiltonian conservative hyperchaotic system is introduced. By conducting basic dynamics analysis and numerical simulation, it is proved that the new system has excellent conservative properties, such as no attractor, phase volume conservation, Hamiltonian energy conservation, and 0 sum of Lyapunov exponents. In addition, the new system has rich dynamic behaviors. It has wide intervals of initial value and wide region of initial condition where it exhibits conservative hyperchaotic orbits. In these wide initial value range, it not only has strong hyperchaotic characteristics and high complexity, but also can observe two completely different energy related multistability phenomena by changing the initial values. Finally, the new system is implemented by using Multisim circuit simulation software and digital signal processor hardware platform.