Hamiltonian Perspective on Compartmental Reaction-Diffusion Networks
Abstract
Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction-diffusion system is a distributed-parameter port-Hamiltonian system on a compact spatial domain. Motivated by the need for computer based design, we offer a spatially consistent discretization of the PDE system and, in a systematic manner, recover a compartmental ODE model on a simplicial triangulation of the spatial domain. Exploring the properties of a balanced weighted Laplacian matrix of the reaction network and the Laplacian of the simplicial complex, we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points. The paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction-diffusion networks.
Cite
@article{arxiv.1212.4999,
title = {Hamiltonian Perspective on Compartmental Reaction-Diffusion Networks},
author = {Marko Seslija and Arjan van der Schaft and Jacquelien M. A. Scherpen},
journal= {arXiv preprint arXiv:1212.4999},
year = {2012}
}