Title data
Wu, Chengshuai ; Grüne, Lars ; Kriecherbauer, Thomas ; Margaliot, Michael:
Behavior of totally positive differential systems near a periodic solution.
In:
Proceedings of the 2021 IEEE Conference on Decision and Control (CDC). 
Austin, Texas, USA
,
2021
.  pp. 31603165
DOI: https://doi.org/10.1109/CDC45484.2021.9683061
This is the latest version of this item.
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Project information
Project financing: 
Israel Science Foundation Grants 

Abstract in another language
A timevarying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tridiagonal with positive entries on the super and subdiagonals. If the vector field of a TPDS is Tperiodic then every bounded trajectory converges to a Tperiodic solution. In particular, when the vector field is timeinvariant 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.
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Behavior of totally positive differential systems near a periodic solution. (deposited 18 Jan 2021 12:19)
 Behavior of totally positive differential systems near a periodic solution. (deposited 14 Feb 2022 10:13) [Currently Displayed]