The concept of equilibrium is powerful and long dominant in the sciences; in physiology, the equilibrium paradigm is embodied in the principle of homeostasis, an equilibrium state that is enforced by negative feedback loops. But physiological quantities are, in fact, not in static equilibrium. Oscillation is another critical form of behavior, seen in both normal physiology and in pathophysiology.

We will review examples of oscillation in normal physiology: gene expression, embryology, hormone regulation, neuronal bursting. We will focus on how mathematical modeling can isolate and identify the mechanisms responsible for the oscillatory behavior.

We will also discuss the why of oscillation: what is the functional role, if any, of these oscillatory processes?

There are also a number of examples of pathological oscillation in physiology and medicine, ranging from muscle tremors to cardiac early-afterdepolarizations to ventricular fibrillation to punctate patterning in arterial calcification. In these cases, mathematical modeling shows us how to design therapeutic interventions and develop new categories of pharmacology.