2010/05/29 by Murad Banaji, Banaji, Murad
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #Petri Nets in System Modeling #math.DS
paper · pdf · doi:10.48550/arxiv.1005.5472
16 pages, 5 figures, BIOPPN conference, Braga 2010
openalex publication_date 2010/05/29 · arxiv created 2010/07/21 · arxiv updated 2010/07/22 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Associated with a chemical reaction network is a natural labelled bipartite multigraph termed an SR graph, and its directed version, the DSR graph. These objects are closely related to Petri nets. The construction of SR and DSR graphs for chemical reaction networks is presented. Conclusions about asymptotic behaviour of the associated dynamical systems which can be drawn easily from the graphs are discussed. In particular, theorems on ruling out the possibility of multiple equilibria or stable oscillation in chemical reaction networks based on computations on SR/DSR graphs are presented. These include both published and new results. The power and limitations of such results are illustrated via several examples.