2026
- ▪E.D. Sontag, "Notes on Mathematical Systems Biology (online)", Online only., 2026. pdfContinuously updated. If the link does not work, then copy/paste this: http://drive.google.com/drive/folders/1lIRqaCPeXMVZGoY-44bBsvtnsHtlRfIO?usp=sharing
2003
- ▪D. Angeli, E.D. Sontag, "Monotone control systems", IEEE Trans. Automat. Control, vol. 48, no. 10, pp. 1684–1698, 2003. pdfErrata are here: http://sontaglab.org/FTPDIR/angeli-sontag-monotone-TAC03-typos.txtMAPK cascades · systems biology · reaction networks · nonlinear stability · dynamical systems · monotone systems
Abstract
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.