Periodicity and Chaos of High-Order Lorenz Systems

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

doi:10.1142/S0218127417501760

Periodicity and Chaos of High-Order Lorenz Systems

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

Seoul National University

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

88 Downloads (Pure)

Abstract

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 language	English
Article number	1750176
Number of pages	11
Journal	International Journal of Bifurcation and Chaos
Volume	27
Issue number	11
DOIs	https://doi.org/10.1142/S0218127417501760
Publication status	Published - 1 Oct 2017
Externally published	Yes

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.

Keywords

chaos
High-order Lorenz systems
nonlinear dynamics
periodicity

ASJC Scopus subject areas

Modelling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

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10.1142/S0218127417501760Licence: CC BY

PublishedFinal published version, 3.96 MBLicence: CC BY

Cite this

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title = "Periodicity and Chaos of High-Order Lorenz Systems",

abstract = "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.",

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AU - Han, Beom Soon

AU - Park, Junho

AU - Seo, Jaemyeong Mango

AU - Baik, Jong Jin

N1 - 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.

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Y1 - 2017/10/1

N2 - 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.

AB - 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.

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Periodicity and Chaos of High-Order Lorenz Systems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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