Title: Quantitative modeling and analysis of bifurcation-induced bursting,
Abstract: Modeling and parameter estimation for neuronal dynamics are often challenging
because many parameters can range over orders of magnitude and are difficult to
measure experimentally. Moreover, selecting a suitable model complexity
requires a sufficient understanding of the model's potential use, such as
highlighting essential mechanisms underlying qualitative behavior or precisely
quantifying realistic dynamics. We present a novel approach that can guide
model development and tuning to achieve desired qualitative and quantitative
solution properties. Our approach relies on the presence of disparate time
scales and employs techniques of separating the dynamics of fast and slow
variables, which are well known in the analysis of qualitative solution
features. We build on these methods to show how it is also possible to obtain
quantitative solution features by imposing designed dynamics for the slow
variables in the form of specified two-dimensional paths in a
bifurcation-parameter landscape.