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Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems

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  • Ge, Zheng-Ming
  • Yi, Chang-Xian

Abstract

In this paper, the chaotic behaviors of a nonlinear damped Mathieu system and of a nonlinear nano resonator system with integral orders and with fractional orders are studied. By applying numerical analyses such as phase portraits, Poincaré maps and bifurcation diagrams, the periodic and chaotic motions are observed. It is found that chaos exists both in the nonlinear damped Mathieu system and in the integral order and fractional order nano resonator systems.

Suggested Citation

  • Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:42-61
    DOI: 10.1016/j.chaos.2005.10.086
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    References listed on IDEAS

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    Cited by:

    1. Deng, Hongmin & Li, Tao & Wang, Qionghua & Li, Hongbin, 2009. "A fractional-order hyperchaotic system and its synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 962-969.
    2. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    3. Ge, Zheng-Ming & Chang, Ching-Ming, 2009. "Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1959-1974.
    4. Yu, Yongguang & Li, Han-Xiong, 2008. "The synchronization of fractional-order Rössler hyperchaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1393-1403.

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