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Chaotic motions of the L-mode to H-mode transition model in tokamak

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Abstract

The chaotic dynamics of the transport equation for the L-mode to H-mode near the plasma in a tokamak is studied in detail with the Melnikov method. The transport equations represent a system with external and parametric excitation. The critical curves separating the chaotic regions and nonchaotic regions are presented for the system with periodically external excitation and linear parametric excitation, or cubic parametric excitation, respectively. The results obtained here show that there exist uncontrollable regions in which chaos always take place via heteroclinic bifurcation for the system with linear or cubic parametric excitation. Especially, there exists a controllable frequency, excited at which chaos does not occur via homoclinic bifurcation no matter how large the excitation amplitude is for the system with cubic parametric excitation. Some complicated dynamical behaviors are obtained for this class of systems.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P. R. China

    Fang-qi Chen  (陈芳启) & Xia Wang  (王霞)

  2. Department of Mechanics, Tianjin University, Tianjin, 300072, P. R. China

    Liang-qiang Zhou  (周良强) & Yu-shu Chen  (陈予恕)

  3. Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin, 300072, P. R. China

    Fang-qi Chen  (陈芳启), Liang-qiang Zhou  (周良强) & Yu-shu Chen  (陈予恕)

Authors
  1. Fang-qi Chen  (陈芳启)
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  2. Liang-qiang Zhou  (周良强)
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  3. Xia Wang  (王霞)
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  4. Yu-shu Chen  (陈予恕)
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Corresponding author

Correspondence to Fang-qi Chen  (陈芳启).

Additional information

Contributed by Yu-shu CHEN

Project supported by the Natural Science Foundation of Tianjin (No. 09JCZDJC26800) and the National Natural Science Foundation of China (No. 10632040)

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Chen, Fq., Zhou, Lq., Wang, X. et al. Chaotic motions of the L-mode to H-mode transition model in tokamak. Appl. Math. Mech.-Engl. Ed. 30, 811–820 (2009). https://doi.org/10.1007/s10483-009-0701-z

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  • DOI: https://doi.org/10.1007/s10483-009-0701-z

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2000 Mathematics Subject Classification

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