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Coexistence of Chaotic and Non-chaotic Orbits in a New Nine-Dimensional Lorenz Model

Title data

Shen, Bo-Wen ; Reyes, Tiffany ; Faghih-Naini, Sara:
Coexistence of Chaotic and Non-chaotic Orbits in a New Nine-Dimensional Lorenz Model.
In: Skiadas, Christos H. ; Lubashevsky, Ihor (ed.): 11th Chaotic Modeling and Simulation International Conference. - Cham : Springer , 2019 . - pp. 239-255
ISBN 978-3-030-15296-3
DOI: https://doi.org/10.1007/978-3-030-15297-0_22

Abstract in another language

In this study, we present a new nine-dimensional Lorenz model (9DLM) that requires a larger critical value for the Rayleigh parameter (a rc of 679.8) for the onset of chaos, as compared to a rc of 24.74 for the 3DLM, a rc of 42.9 for the 5DLM, and a rc 116.9 for the 7DLM. Major features within the 9DLMinclude: (1) the coexistence of chaotic and non-chaotic orbits with moderate Rayleigh parameters, and (2) the coexistence of limit cycle/torus orbits and spiral sinks with large Rayleigh parameters. Version 2 of the 9DLM, referred to as the 9DLM-V2, is derived to show that: (i) based on a linear stability analysis, two non-trivial critical points are stable for all Rayleigh parameters greater than one; (ii) under non-dissipative and linear conditions, the extended nonlinear feedback loop produces four incommensurate frequencies; and (iii) for a stable orbit, small deviations away from equilibrium (e.g., the stable critical point) do not have a significant impact on orbital stability. Based on our results, we suggest that the entirety of weather is a superset that consists of both chaotic and non-chaotic processes.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: Lorenz model; Limit cycle; Nonlinear feedback loop; Coexistence; Incommensurate frequencies; Aggregated negative feedback
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Lehrstuhl Wissenschaftliches Rechnen
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics >
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > >
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Result of work at the UBT: No
DDC Subjects: 000 Computer Science, information, general works
000 Computer Science, information, general works > 004 Computer science
500 Science
500 Science > 500 Natural sciences
500 Science > 510 Mathematics
500 Science > 550 Earth sciences, geology
600 Technology, medicine, applied sciences
600 Technology, medicine, applied sciences > 600 Technology
Date Deposited: 14 Nov 2019 08:00
Last Modified: 14 Nov 2019 08:00
URI: https://eref.uni-bayreuth.de/id/eprint/53226