2021/01/15 by Chengshuai Wu, Wu, Chengshuai, Lars Gruene +5
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.2101.06027
openalex publication_date 2021/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.