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Volume 25 Issue 2
Feb.  1999
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Journal of Beijing University of Aeronautics and Astronautics  > 1999  >  25(2): 225-228.
Gan Chunbiao, Lu Qishao. Asymptotic Solutions, Bifurcations and Chaosof Slow-Varying System[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(2): 225-228. (in Chinese)
Citation: Gan Chunbiao, Lu Qishao. Asymptotic Solutions, Bifurcations and Chaosof Slow-Varying System[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(2): 225-228. (in Chinese)
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Asymptotic Solutions, Bifurcations and Chaosof Slow-Varying System

  • Beijing University of Aeronautics and Astronautics,Dept. of Applied Mathematics and Physics

  • Received Date: 06 Nov 1997
  • Publish Date: 28 Feb 1999
    Abstract
  • A non-linear system with slow-varying parameters is dealt with.By using perturbation theory,the asymptotic expressions of periodic solutions are obtained and compared with the numerical results. By the phase portraits, power spectrum analysis, bifurcation diagram and computation of the largest Lyapunov exponent,the process from period-doubling bifurcations to chaos is studied. It is shown that, following the variation of the system's small parameter, the motion of the system becomes chaotic through a similar bifurcation as that in the Lorenz model. Moreover, it is not difficult to find that the system is more tractable than the Lorenz model and the analytic form of the symmetric periodic solutions can be got easily.

     

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  • 1. Collinge I R, Ockendon J R. Transition resonance of a Duffing oscillator. SIAM J Appl Math, 1979, 15:350~357 2. Moslehy F A, Evan-Iwanowski R M. The effects of nonstationary processes on chaotic and regular responses of the Duffing oscillator. Int J Non-Linear Mech, 1991, 26:61~71 3. Rahman Z, Burton T D. Large amplitude primary and superharmonic resonance in the Duffing oscillator. J Sound and Vibration, 1986, 110:363~380 4. Jordan D W, Smith P. Non-linear ordinary differential equations. 2nd ed. Oxford:Clarendon Press, 1987 5. Wiggins S. Introduction to applied non-linear dynamical systems and chaos. 2nd ed.Berlin:Springer-Verlag, 1991 6. Suire G, Cederbaum G. Periodic and chaos behavior of viscoelastic non-linear (elastic) bars under harmonic excitations. Int J Mech Sci, 1995, 37:753~772
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