  Many systems in biology, physics and engineering can be described by systems
of ordinary differential equation containing many parameters. When studying the
dynamic behavior of these large, nonlinear systems, it is useful to identify
and characterize the steady-state solutions as the model parameters vary, a
technically challenging problem in a high-dimensional parameter landscape.
Rather than simply determining the number and stability of steady-states at
distinct points in parameter space, we decompose the parameter space into
finitely many regions, the steady-state solutions being consistent within each
distinct region. From a computational algebraic viewpoint, the boundary of
these regions is contained in the discriminant locus. We develop global and
local numerical algorithms for constructing the discriminant locus and
classifying the parameter landscape. We showcase our numerical approaches by
applying them to molecular and cell-network models.
