Sloppy Model Analysis near Bifurcations

In dynamical systems, bifurcations occur when a small change in parameter values results in an obvious topological change in system behavior. They are useful for identifying "tipping points" between qualitatively different types of behaviors, such as phase transitions in matter 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 one of only a few "normal forms", 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.