2015/02/08 by Arjan van der Schaft, van der Schaft, Arjan, Shodhan Rao +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #math.DS #math.OC
paper · pdf · doi:10.48550/arxiv.1502.02247
18 pages
arxiv created 2015/02/08 · openalex publication_date 2015/02/08 · arxiv updated 2015/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in chemical reaction network theory, and which directly relates to the thermodynamics of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This directly leads to the characterization of the set of equilibria and their stability. Both the form of the dynamics and the deduced dynamical behavior are very similar to consensus dynamics. The assumption of complex-balancedness is revisited from the point of view of Kirchhoff's Matrix Tree theorem, providing a new perspective. Finally, using the classical idea of extending the graph of chemical complexes by an extra 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action outflows is given.