Rendering a subcritical Hopf bifurcation supercritical

Abstract

It is demonstrated experimentally and theoretically that through the use of a nonlinear feedback controller, one can render a subcritical Hopf bifurcation supercritical and thus dramatically modify the nature of the flow in a thermal convection loop heated from below and cooled from above. In particular, we show that the controller can replace the naturally occurring chaotic motion with a stable, periodic limit cycle. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to counteract such deviations.