@inproceedings{93e8049104644a168b9663f574e00a64,
title = "Behavior of Totally Positive Differential Systems Near a Periodic Solution",
abstract = "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 equilibrium. We use the spectral theory of oscillatory matrices to analyze the behavior near a periodic solution of a TPDS. This yields explicit 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.",
author = "Chengshuai Wu and Lars Grune and Thomas Kriecherbauer and Michael Margaliot",
note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; 60th IEEE Conference on Decision and Control, CDC 2021 ; Conference date: 13-12-2021 Through 17-12-2021",
year = "2021",
doi = "https://doi.org/10.1109/CDC45484.2021.9683061",
language = "الإنجليزيّة",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "3160--3165",
booktitle = "60th IEEE Conference on Decision and Control, CDC 2021",
address = "الولايات المتّحدة",
}