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Many systems in biology, physics and engineering can be described by systemsof ordinary differential equation containing many parameters. When studying thedynamic behavior of these large, nonlinear systems, it is useful to identifyand characterize the steady-state solutions as the model parameters vary, atechnically challenging problem in a high-dimensional parameter landscape.Rather than simply determining the number and stability of steady-states atdistinct points in parameter space, we decompose the parameter space intofinitely many regions, the steady-state solutions being consistent within eachdistinct region. From a computational algebraic viewpoint, the boundary ofthese regions is contained in the discriminant locus. We develop global andlocal numerical algorithms for constructing the discriminant locus andclassifying the parameter landscape. We showcase our numerical approaches byapplying them to molecular and cell-network models.

Decomposing the parameter space of biological networks via a numerical discriminant approach