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On period doubling bifurcations of cycles and the harmonic balance method

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  • Itovich, Griselda R.
  • Moiola, Jorge L.

Abstract

This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method.

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  • Itovich, Griselda R. & Moiola, Jorge L., 2006. "On period doubling bifurcations of cycles and the harmonic balance method," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 647-665.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:3:p:647-665
    DOI: 10.1016/j.chaos.2005.04.061
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    Cited by:

    1. Pei, Lijun & Wu, Fanxin, 2021. "Periodic solutions, chaos and bi-stability in the state-dependent delayed homogeneous Additive Increase and Multiplicative Decrease/Random Early Detection congestion control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 871-887.

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