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 | |
| 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.Funding
The authors are grateful to two reviewers for providing valuable comments on this work. This work was funded by the Korea Meteorological Administration Research and Development Program under grant KMIPA 2015–5100 and also by Mid-career Researcher Program through National Research Foundation (NRF) grant funded by the Ministry of Science, ITC and Future Planning (MSIP) (2016R1A2B2013549).
Keywords
- chaos
- High-order Lorenz systems
- nonlinear dynamics
- periodicity
ASJC Scopus subject areas
- Modelling and Simulation
- Engineering (miscellaneous)
- General
- Applied Mathematics