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Bifurcations of periodic orbits and chaos in damped and driven morse oscillator

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  • Jing, Zhujun
  • Deng, Jin
  • Yang, Jianping

Abstract

Damped and driven Morse oscillator is investigated in detail. The existence and the bifurcations of harmonics, second-order and third-order subharmonics, second-order and third-order superharmonics are given by using second-order averaging method. The numerical simulations including bifurcation diagrams in three- and two-dimensional spaces, maximum Lyapunov exponents, phase portraits, poincaré map, exhibit the complicated dynamical behaviors. We show the period-doubling and reverse period-doubling routes to chaos, the onset of chaos, reverse period-6 bubble, period-4 bubble, period-one orbit suddenly switching to an invariant torus, chaotic regions with invariant torus or with complicated periodic windows, or with interior crisis, nice chaotic attractors, non-attracting chaotic set, and a new type of non-chaotic attractors. Moreover, the influence of initial conditions on the dynamical behavior is considered. Combining the existing results of Wiggins et al. with the new results reported in this paper, a more complete description of the system is now obtained.

Suggested Citation

  • Jing, Zhujun & Deng, Jin & Yang, Jianping, 2008. "Bifurcations of periodic orbits and chaos in damped and driven morse oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 486-505.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:3:p:486-505
    DOI: 10.1016/j.chaos.2006.05.038
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