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Quasi-Periodic Orbits in the Five-Dimensional Nondissipative Lorenz Model : the Role of the Extended Nonlinear Feedback Loop

Title data

Faghih-Naini, Sara ; Shen, Bo-Wen:
Quasi-Periodic Orbits in the Five-Dimensional Nondissipative Lorenz Model : the Role of the Extended Nonlinear Feedback Loop.
In: International Journal of Bifurcation and Chaos. Vol. 28 (2018) Issue 6 . - No. 1850072.
ISSN 0218-1274
DOI: https://doi.org/10.1142/S0218127418500724

Abstract in another language

A recent study suggested that the nonlinear feedback loop (NFL) of the three-dimensional nondissipative Lorenz model (3D-NLM) serves as a nonlinear restoring force by producing nonlinear oscillatory solutions as well as linear periodic solutions near a nontrivial critical point. This study discusses the role of the extension of the NFL in producing quasi-periodic trajectories using a five-dimensional nondissipative Lorenz model (5D-NLM). An analytical solution to the locally linear 5D-NLM is first obtained to illustrate the association of the extended NFL and two incommensurate frequencies whose ratio is irrational, yielding a quasi-periodic solution. The quasi-periodic solution trajectory moves endlessly on a torus but never intersects itself.
While the NFL of the 3D-NLM consists of a pair of downscaling and upscaling processes, the extended NFL within the 5D-NLM additionally introduces two new pairs of downscaling and upscaling processes that are enabled by two high wavenumber modes. One pair of downscaling and upscaling processes provides a two-way interaction between the original (primary) Fourier modes of the 3D-NLM and the newly-added (secondary) Fourier modes of the 5D-NLM. The other pair of downscaling and upscaling processes involves interactions amongst the secondary modes. By comparing the numerical simulations using one- and two-way interactions, we illustrate that the two-way interaction is crucial for producing the quasi-periodic solution. A follow-up study using a 7D nondissipative LM shows that a further extension of NFL, which may appear throughout the spatial mode-mode interactions rooted in the nonlinear temperature advection, is capable of producing one more incommensurate frequency.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Nondissipative Lorenz model; nonlinear feedback loop; quasi-periodicity
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 Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Research Institutions
Research Institutions > Research Centres
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 > 510 Mathematics
500 Science > 550 Earth sciences, geology
600 Technology, medicine, applied sciences
600 Technology, medicine, applied sciences > 600 Technology
Date Deposited: 12 Nov 2019 07:31
Last Modified: 13 Nov 2019 14:23
URI: https://eref.uni-bayreuth.de/id/eprint/53175