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Behavior of totally positive differential systems near a periodic solution

Title data

Wu, Chengshuai ; Grüne, Lars ; Kriecherbauer, Thomas ; Margaliot, Michael:
Behavior of totally positive differential systems near a periodic solution.
Bayreuth ; Tel Aviv , 2021 . - 6 pages

Official URL: Volltext

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Project information

Project financing: Israel Science Foundation Grants

Abstract in another language

A time-varying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tri-diagonal with positive entries on the super- and sub-diagonals. If the vector field of a TPDS is T-periodic then every bounded trajectory converges to a T-periodic solution. In particular, when the vector field is time-invariant every bounded trajectory of a TPDS converges to an equlbrium. Here, we use the spectral theory of oscillatory matrices to analyze the behavior near a periodic solution of a TPDS. This yields information on the perturbation directions that lead to the fastest and slowest convergence to or divergence from the periodic solution. We demonstrate the theoretical results using a model from systems biology called the ribosome flow model.

Further data

Item Type: Preprint, postprint
Refereed: Yes
Keywords: Totally positive differential system; Floquet theory; Perturbations
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 > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) - Univ.-Prof. Dr. Thomas Kriecherbauer
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 570 Life sciences, biology
Date Deposited: 18 Jan 2021 12:19
Last Modified: 16 Mar 2021 14:24
URI: https://eref.uni-bayreuth.de/id/eprint/61964