Sloppy model analysis of dynamical systems near bifurcations*

In dynamical systems, bifurcations refer to topological changes in phase space trajectories in response to relatively small changes in parameter values. They are useful for identifying tipping points between qualitatively different types of behaviors such a phase transitions or from regulated to cancerous cellular pathways. Bifurcations are classified by the nature of the topological change in phase space with classes being typified by a "normal form", indicating that only a few parameters are responsible for driving a system through a bifurcation. Sloppy models provide a framework for identifying relevant parameters in a data-driven way. We apply sloppy model analysis to several dynamical systems near their bifurcations. We show that after an appropriate coarse-graining procedure, sloppy model analysis is able to correctly identify the bifurcation parameters. This suggests that sloppy model analysis can be used to identify the relevant control knobs in multi-parameter models of complex dynamical systems in a data-driven way.