# BiRNe: Symbolic bifurcation analysis of reaction networks with Python Source: [BiRNe: Symbolic bifurcation analysis of reaction networks with Python]() Collection index: [llms.txt]() Data updated: 2025-11-20T05:03:42.417Z Authors: Richard Golnik, Thomas Gatter, Peter F. Stadler, Nicola Vassena Published: 2025-11-18T12:33:58.000Z ## Abstract Computer algebra methods for analyzing reaction networks often rely on the assumption of mass-action kinetics, which transform the governing ODEs into polynomial systems amenable to techniques such as Gr\\"obner basis computation and related algebraic tools. However, these methods face significant computational complexity, limiting their applicability to relatively small networks involving only a handful of species. In contrast, building on recent theoretical advances, we introduce here \\textsc{BiRNe} (BIfurcations in Reaction NEtworks) Python module, which relies on a symbolic approach designed to detect bifurcations in larger reaction networks (up to 10-20 species, depending on the network's connectivity) equipped with parameter-rich kinetics. This class includes enzymatic kinetics such as Michaelis--Menten, ligand-binding kinetics like Hill functions, and generalized mass-action kinetics. For a given network, the current algorithm identifies all minimal autocatalytic subnetworks and fully characterizes the presence of bifurcations associated with zero eigenvalues, thus determining whether the network admits multistationarity. It also detects oscillatory bifurcations arising from positive-feedback structures, capturing a significant class of possible oscillations. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()