Book chapter
Guaranteeing Spatial Uniformity in Reaction-Diffusion Systems Using Weighted L2 Norm Contractions
A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations, pp.73-101
Springer Netherlands
07/04/2014
DOI: 10.1007/978-94-017-9041-3_3
Abstract
We present conditions that guarantee spatial uniformity of the solutions of reaction-diffusion partial differential equations. These equations are of central importance to several diverse application fields concerned with pattern formation. The conditions make use of the Jacobian matrix and Neumann eigenvalues of elliptic operators on the given spatial domain. We present analogous conditions that apply to the solutions of diffusively-coupled networks of ordinary differential equations. We derive numerical tests making use of linear matrix inequalities that are useful in certifying these conditions. We discuss examples relevant to enzymatic cell signaling and biological oscillators. From a systems biology perspective, the paper’s main contributions are unified verifiable relaxed conditions that guarantee spatial uniformity of biological processes.
Details
- Title: Subtitle
- Guaranteeing Spatial Uniformity in Reaction-Diffusion Systems Using Weighted L2 Norm Contractions
- Creators
- Zahra Aminzare - Department of Mathematics, Rutgers University, Piscataway, USAYusef Shafi - Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USAMurat Arcak - Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USAEduardo D Sontag - Department of Mathematics, Rutgers University, Piscataway, USA
- Resource Type
- Book chapter
- Publication Details
- A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations, pp.73-101
- DOI
- 10.1007/978-94-017-9041-3_3
- Publisher
- Springer Netherlands; Dordrecht
- Language
- English
- Date published
- 07/04/2014
- Academic Unit
- Iowa Neuroscience Institute; Mathematics
- Record Identifier
- 9984065884902771
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