Dynamical analysis of a third-order nonlinear amplitude equation for plasma torch

Der-Cherng Liaw*, Shih Tse Chang, Heng Yi Li, Chin Ching Tzeng, Shiaw Huei Chen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper focuses on the analysis of a third-order nonlinear amplitude equation for finding possible dynamical behavior appearing in the plasma torch. The analysis was achieved by employing system linearization and bifurcation theorems. Local bifurcation analysis for a class of the third-order nonlinear systems was studied in (Liaw et al, 2009) to solve for the existence conditions of pitchfork stationary bifurcation, Andronov-Hopf bifurcations, period-doubling, and torus bifurcation. Numerical simulations were also obtained to study the nonlocal dynamical phenomena and the linkage among bifurcation phenomena and chaotic behavior. In this paper, those analyses will be extended to the more general cases. The scenarios for the possible nonlinear behavior in a third-order amplitude equation are justified for the plasma torch with respect to the variation of system parameters via the numerical simulations, which might provide a guide to determine the occurrence of nonlinear phenomena in the practical application of the plasma torch.

Original languageEnglish
Title of host publicationProceedings of SICE Annual Conference 2010, SICE 2010 - Final Program and Papers
PublisherSociety of Instrument and Control Engineers (SICE)
Number of pages6
ISBN (Print)9784907764364
StatePublished - 1 Jan 2010

Publication series

NameProceedings of the SICE Annual Conference


  • Andronov-Hopf bifurcation
  • Chaotic behavior
  • Perioddoubling
  • Plasma torch
  • Torus bifurcation

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