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Biomolecular Feedback Systems$
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Domitilla Del Vecchio and Richard M. Murray

Print publication date: 2014

Print ISBN-13: 9780691161532

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691161532.001.0001

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Analysis of Dynamic Behavior

Analysis of Dynamic Behavior

Chapter:
(p.89) Chapter 3 Analysis of Dynamic Behavior
Source:
Biomolecular Feedback Systems
Author(s):

Domitilla Del Vecchio

Richard M. Murray

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691161532.003.0003

This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the dynamics of a system using the input/output modeling formalism described in Chapter 1 and then studies the “robustness” of the system of a given function of the circuit. The chapter then discusses some of the underlying ideas for how to model biological oscillatory behavior, focusing on those types of oscillations that are most common in biomolecular systems. Hereafter, the chapter explores how the location of equilibrium points, their stability, their regions of attraction, and other dynamic phenomena vary based on the values of the parameters in a model. Finally, methods for reducing the complexity of the models that are introduced in this chapter are reviewed.

Keywords:   dynamical systems, feedback control theory, biological circuits, modeling formalism, robustness, biological oscillations, equilibrium points, deterministic models

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