Research in Nonlinear Dynamics
"Using a term like nonlinear science is like referring to the bulk of zoology as the study of non-elephant animals." (Stanislaw Ulam)
Nonlinearity quite commonly arises through the collective behavior of even the simplest systems: it is insufficient to simply (linearly) add the effects of the components. Instead, the interactions between the components lead to such emergent phenomena as chaos, solitons, fractals, and meta/multi-stability. The resulting dynamics can be highly unpredictable, even though the underlying physics is deterministic.