A structural classification of candidate oscillators and multistationary systems

Molecular systems are uncertain: the variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In particular, starting with Thomas' conjectures, loop-based criteria have been largely used to characterize oscillatory and multistationary dynamic outcomes in systems with a sign definite Jacobian.\n\nWe build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors based on parameter-free criteria. We propose a cla