1.
RHYTHMS IN HUMAN NATURE
10
Glass and Mackay illustrate simple perturbations in an experiment that
analyzes
“The effects of a brief
electrical shock delivered to an aggregate of spontaneously beating
cells derived from the ventricles of an embryonic chick heart. In
response to a brief electrical stimulus, there is a resetting of the
phase of subsequent action potentials, but the original cycle time is
reestablished within several beats… Poincare called such oscillations
stable limit cycles… If, on the other hand, a small perturbation
induces a change in the dynamics so that the original dynamics are not
reestablished, then the steady state or limit cycle is unstable…. Any
value of a parameter at which the number and/or stability of steady
states and cycles change is called a bifurcation point and the system
is said to undergo a bifurcation… Since small changes in parameters
lead to qualitatively different dynamics at bifurcation points, systems
are not structurally stable at bifurcation points.” ^{3}
Arthur
Winfree, a pioneering biophysicist and chronobiologist, makes the case
that small perturbations to rhythms, when precisely timed, can have big
effects. In his studies on cardiac arrhythmias, especially ventricular
fibrillation, he observed, “a small local depolarization can trigger
transition to fibrillation…If the stimulus is too big or too small or
wrongly timed, it won’t work. There is an atrial vulnerable phase and,
later, a ventricular vulnerable phase.” ^{4}
