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arXiv · 1212.4999

Hamiltonian Perspective on Compartmental Reaction-Diffusion Networks

Marko Seslija·Arjan van der Schaft·Jacquelien M. A. Scherpen
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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.

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Marko Seslija, Arjan van der Schaft, Jacquelien M. A. Scherpen. 2012-12-20. Hamiltonian Perspective on Compartmental Reaction-Diffusion Networks. https://arxiv.org/abs/1212.4999

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