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

4 Citations (Scopus)
5 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)2889-2912
Number of pages24
JournalNonlinear Dynamics
Volume110
Issue number3
Early online date19 Aug 2022
DOIs
Publication statusPublished (in print/issue) - 30 Nov 2022

Bibliographical note

Funding Information:
This work is supported by the National Key Technology R &D Program of China (No. 2018YFC0910 500), the National Natural Science Foundation of China (Nos. 61425002, 61751203, 61772100, 61972266, 61802040), LiaoNing Revitalization Talents Program (No. XLYC2008017), the Innovation and Entrepreneurship Team of Dalian University (No.XQN202008), Natural Science Foundation of Liaoning Province (Nos. 2021-MS-344, 2021-KF-11-03), Scientific Research Fund of Liaoning Provincial Education Department (No. LJKZ1186), Dalian University Scientific Research Platform Program (No. 202101YB02). Shihua Zhou and Qiang Zhang are the corresponding authors of this paper.

Funding Information:
The National Key Technology R &D Program of China (No. 2018YFC0910500), the National Natural Science Foundation of China (Nos. 61425002, 61751203, 61772100, 61972266, 61802040), LiaoNing Revitalization Talents Program (No. XLYC2008017), the Innovation and Entrepreneurship Team of Dalian University (No.XQN202008), Natural Science Foundation of Liaoning Province (Nos. 2021-MS-344, 2021-KF-11-03), Scientific Research Fund of Liaoning Provincial Education Department (No. LJKZ1186), Dalian University Scientific Research Platform Program (No. 202101YB02).

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.

Keywords

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

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