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

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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.

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The authors declare that the data supporting the findings of this study are available within the article.

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Acknowledgements

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

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).

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Authors and Affiliations

  1. Key Laboratory of Advanced Design and Intelligent Computing, Ministry of Education, School of Software Engineering, Dalian University, Dalian, 116622, People’s Republic of China

    Qing Dong, Shihua Zhou & Qiang Zhang

  2. School of Computer Science and Technology, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Qiang Zhang

  3. Knowledge Engineering and Discovery Research Institute, Auckland University of Technology, Auckland, 1010, New Zealand

    Nikola K. Kasabov

  4. Intelligent Systems Research Center, Ulster University, Londonderry, BT52 1SA, UK

    Nikola K. Kasabov

  5. Auckland Bioengineering Institute (ABI), The University of Auckland, Auckland, 1010, New Zealand

    Nikola K. Kasabov

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  1. Qing Dong
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Dong, Q., Zhou, S., Zhang, Q. et al. A class of 5D Hamiltonian conservative hyperchaotic systems with symmetry and multistability. Nonlinear Dyn 110, 2889–2912 (2022). https://doi.org/10.1007/s11071-022-07735-6

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