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- W4301434205 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." @default.
- W4301434205 created "2022-10-05" @default.
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- W4301434205 date "2012-12-20" @default.
- W4301434205 modified "2023-10-14" @default.
- W4301434205 title "Hamiltonian Perspective on Compartmental Reaction-Diffusion Networks" @default.
- W4301434205 doi "https://doi.org/10.48550/arxiv.1212.4999" @default.
- W4301434205 hasPublicationYear "2012" @default.
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