Periodicity and Chaos of High-Order Lorenz Systems

Sungju Moon, Beom Soon Han, Junho Park, Jaemyeong Mango Seo, Jong Jin Baik

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)
27 Downloads (Pure)


High-order Lorenz systems with five, six, eight, nine, and eleven equations are derived by choosing different numbers of Fourier modes upon truncation. For the original Lorenz system and for the five high-order Lorenz systems, solutions are numerically computed, and periodicity diagrams are plotted on (σ,r) parameter planes with σ,r [0, 1000], and b = 8/3. Dramatic shifts of patterns are observed among periodicity diagrams of different systems, including the appearance of expansive areas of period 2 in the fifth-, eighth-, ninth-, and 11th-order systems and the disappearance of the onion-like structure beyond order 5. Bifurcation diagrams along with phase portraits offer a closer look at the two phenomena.

Original languageEnglish
Article number1750176
Number of pages11
JournalInternational Journal of Bifurcation and Chaos
Issue number11
Publication statusPublished - 1 Oct 2017
Externally publishedYes

Bibliographical note

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.


  • chaos
  • High-order Lorenz systems
  • nonlinear dynamics
  • periodicity

ASJC Scopus subject areas

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


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