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Hyperchaos in constrained Hamiltonian system and its control

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Abstract

This paper first formulates a Hamiltonian system with hyperchaotic phenomena and investigates the equilibrium point and double Hopf bifurcation of the system. We obtain the result that the Hamiltonian system has hyperchaotic behaviors when any system parameter varies. The influences of holonomic constraint and nonholonomic constraint on the equilibrium points, invariance and the hyperchaotic state of the Hamiltonian system are then studied. Finally, we achieve the hyperchaotic control of the Hamiltonian system by introducing the constraint method. The studies indicate that the constraint can not only change the Hamiltonian system from hyperchaotic state to periodic state or chaotic state, but also make the Hamiltonian system become globally asymptotically stable. Numerical simulations, including Lyapunov exponents, bifurcation diagrams, Poincaré maps and phase portraits for systems, exhibit the complex dynamical behaviors.

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Acknowledgements

Project is supported by the National Natural Science Foundation of China (Grant No. 11672032), Youth Science Foundations of Education Department of Hebei Province (No. QN2016265), Hebei Special Foundation “333 talent project” (No. A2016001123) and Scientific Research Funds of Hebei Institute of Architecture and Civil Engineering (Nos. 2016XJJQN03, 2016XJJYB05).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Junhong Li & Huibin Wu

  2. Department of Mathematics and Sciences, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, 075000, Hebei, China

    Junhong Li

  3. Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, 100081, China

    Huibin Wu

  4. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Fengxiang Mei

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  1. Junhong Li
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Correspondence to Junhong Li.

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Li, J., Wu, H. & Mei, F. Hyperchaos in constrained Hamiltonian system and its control. Nonlinear Dyn 94, 1703–1720 (2018). https://doi.org/10.1007/s11071-018-4451-3

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