2012/12/20 by Marko Šešlija, Arjan van der Schaft, Seslija, Marko +3
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Pattern Formation and Solitons (nlin.PS) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1212.4999
openalex publication_date 2012/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.