Simplification of the quasiperiodic route to chaos in agonist-induced vasomotion by iterative circle maps

Rabbit ear resistance artery vasomotion phase space portraits were used to derive iterative maps via the Poincare section. The vasomotion approximates the movement on the surface of a torus. In a quasiperiodic system, the strong coupling of two oscillators becomes locked into a rational ratio which can be used as the basis for a staircase function. Derivation of this function proves that frequency-locked states and the associated quasiperiodic transition to chaos conforms to an iterative circle map.