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On the gain of entrainment in a class of weakly contractive bilinear control systems with applications to the master equation and the ribosome flow model

Title data

Katz, Rami ; Kriecherbauer, Thomas ; Grüne, Lars ; Margaliot, Michael:
On the gain of entrainment in a class of weakly contractive bilinear control systems with applications to the master equation and the ribosome flow model.
Bayreuth ; Tel Aviv , 2023 . - 42 p.
DOI: https://doi.org/10.48550/arXiv.2307.03568

Official URL: Volltext

Project information

Project title:
Project's official title
Project's id
Analysis of Random Transport in Chains using Modern Tools from Systems and Control Theory
GR 1569/24-1, KR 1673/7-1

Project financing: Deutsche Forschungsgemeinschaft
Israel Science Foundation Grants

Abstract in another language

We consider a class of bilinear weakly contractive systems that entrain to periodic excitations. Entrainment is important in many natural and artificial processes. For example, in order to function properly synchronous generators must entrain to the frequency of the electrical grid, and biological organisms must entrain to the 24h solar day. A dynamical system has a positive gain of entrainment (GOE) if entrainment also yields a larger output, on average. This property is important in many applications from the periodic operation of bioreactors to the periodic production of proteins during the cell cycle division process. We derive a closed-form formula for the GOE to first-order in the control perturbation. This is used to show that in the class of systems that we consider the GOE is always a higher-order phenomenon. We demonstrate the theoretical results using two applications: the master equation and a model from systems biology called the ribosome flow model, both with time-varying and periodic transition rates.

Further data

Item Type: Preprint, postprint
Refereed: No
Keywords: gain of entrainment; higher-order phenomenon; master equation; Ribosome flow model
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 > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Research Institutions
Research Institutions > Central research institutes
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 570 Life sciences, biology
Date Deposited: 11 Jul 2023 06:21
Last Modified: 11 Jul 2023 06:21
URI: https://eref.uni-bayreuth.de/id/eprint/86070