  High-dimensional systems that have a low-dimensional dominant behavior allow
for model reduction and simplified analysis. We use differential analysis to
formalize this important concept in a nonlinear setting. We show that dominance
can be studied through linear dissipation inequalities and an interconnection
theory that closely mimics the classical analysis of stability by means of
dissipativity theory. In this approach, stability is seen as the limiting
situation where the dominant behavior is 0-dimensional. The generalization
opens novel tractable avenues to study multistability through 1-dominance and
limit cycle oscillations through 2-dominance.
