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Dynamic Analysis of a Particle Motion System

Author

Listed:
  • Ning Cui

    (Department of Mathematics and Sciences, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou 075000, Hebei Province, China)

  • Junhong Li

    (Department of Mathematics and Sciences, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou 075000, Hebei Province, China
    School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

This paper formulates a new particle motion system. The dynamic behaviors of the system are studied including the continuous dependence on initial conditions of the system’s solution, the equilibrium stability, Hopf bifurcation at the equilibrium point, etc. This shows the rich dynamic behaviors of the system, including the supercritical Hopf bifurcations, subcritical Hopf bifurcations, and chaotic attractors. Numerical simulations are carried out to verify theoretical analyses and to exhibit the rich dynamic behaviors.

Suggested Citation

  • Ning Cui & Junhong Li, 2018. "Dynamic Analysis of a Particle Motion System," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:7-:d:192329
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    References listed on IDEAS

    as
    1. P. Gaspard & M. E. Briggs & M. K. Francis & J. V. Sengers & R. W. Gammon & J. R. Dorfman & R. V. Calabrese, 1998. "Experimental evidence for microscopic chaos," Nature, Nature, vol. 394(6696), pages 865-868, August.
    2. Kuwana, Célia Mayumi & de Oliveira, Juliano A. & Leonel, Edson D., 2014. "A family of dissipative two-dimensional mappings: Chaotic, regular and steady state dynamics investigation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 458-465.
    3. D. J. Pine & J. P. Gollub & J. F. Brady & A. M. Leshansky, 2005. "Chaos and threshold for irreversibility in sheared suspensions," Nature, Nature, vol. 438(7070), pages 997-1000, December.
    Full references (including those not matched with items on IDEAS)

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