## 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

## 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.