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

Qing Dong, Shihua Zhou, Qiang Zhang, Nikola Kasabov

Research output: Contribution to journalArticlepeer-review


Conservative chaos systems have been investigated owing to their special advantages. Taking symmetry as a starting point, this study proposes a class of ve-dimensional(5D) conservative hyperchaotic systems by constructing a generalized Hamiltonian conservative system. The proposed systems can have dierent 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 veried 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 dierent numbers of coexisting orbits under the same energy. And, this type of system can also exhibit the coexistence of innite orbits of dierent energies. Finally, the National Institute of Standards and Technology tests conrmed 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.

Original languageEnglish
Article numberNODY-D-22-01270R1 - [EMID:4e6c36d421de273f]
Pages (from-to)1-24
Number of pages24
JournalNonlinear Dynamics
Publication statusPublished - 19 Aug 2022


  • Hamiltonian conservative hyperchaotic system
  • time-reversal symmetry
  • equal-energy coexisting orbit
  • extreme multistability


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