Differential equations and dynamical systems
Differential equations and dynamical systems
Simulating, Analyzing, and Animating Dynamical Systems: A Guide Toi Xppaut for Researchers and Students
Stability of Time-Delay Systems
Stability of Time-Delay Systems
Critical delays and polynomial eigenvalue problems
Journal of Computational and Applied Mathematics
Graphical methods for analysing feedback in biological networks-A survey
International Journal of Systems Science - Dynamics Analysis of Gene Regulatory Networks
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Differential equation models for biological oscillators are often not robust with respect to parameter variations. They are based on chemical reaction kinetics, and solutions typically converge to a fixed point. This behavior is in contrast to real biological oscillators, which work reliably under varying conditions. Moreover, it complicates network inference from time series data. This paper investigates differential equation models for biological oscillators from two perspectives. First, we investigate the effect of time delays on the robustness of these oscillator models. In particular, we provide sufficient conditions for a time delay to cause oscillations by destabilizing a fixed point in two-dimensional systems. Moreover, we show that the inclusion of a time delay also stabilizes oscillating behavior in this way in larger networks. The second part focuses on the inverse problem of estimating model parameters from time series data. Bifurcations are related to nonsmoothness and multiple local minima of the objective function.