Periodic and Chaotic Dynamics of the Ehrhard-Müller System

Junho Park, Hyunho Lee, Jong Jin Baik

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


This paper investigates nonlinear ordinary differential equations of the Ehrhard-Müller system which describes natural convection in a single-phase loop in the presence of nonsymmetric heating. Stability and dynamics of periodic and chaotic behaviors of the equations are investigated and the periodicity diagram is obtained in wide ranges of parameters. Regimes of both periodic and chaotic solutions are observed with complex behaviors such that the periodic regimes enclose the chaotic regime while they are also immersed inside the chaotic regime with various shapes. An asymptotic analysis is performed for sufficiently large parameters to understand the enclosure by the periodic regimes and asymptotic limit cycles are obtained to compare with limit cycles obtained from numerical results.

Original languageEnglish
Article number1630015
JournalInternational Journal of Bifurcation and Chaos
Issue number6
Publication statusPublished - 15 Jun 2016
Externally publishedYes


  • asymptotic analysis
  • chaotic dynamics
  • Ehrhard-Müller system
  • periodicity diagram
  • stability analysis

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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