TY - GEN
T1 - Behavior of Totally Positive Differential Systems Near a Periodic Solution
AU - Wu, Chengshuai
AU - Grune, Lars
AU - Kriecherbauer, Thomas
AU - Margaliot, Michael
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85126053202&partnerID=8YFLogxK
U2 - 10.1109/CDC45484.2021.9683061
DO - 10.1109/CDC45484.2021.9683061
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AN - SCOPUS:85126053202
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3160
EP - 3165
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -