Optimal Phase-to-Phase Control of Chemical Oscillations

We investigate the effectiveness of phase manipulation of chemical oscillations with open loop control based on phase model description. Minimum-power controls are applied to alter the phase of the oscillation from an arbitrary initial value to a desired value within one oscillatory cycle. We demonstrate the applicability of the controls by changing the instantaneous oscillation period of an oscillatory electrochemical system from an arbitrary predetermined initial phase. The experiments showed that the instantaneous period can be effectively modified from any initial phase for a range of ±30% of the natural (uncontrolled) period. Although the method is tested with electrochemical oscillations, the phase model description is general and holds promise in applications in a wide range of disciplines, for example, circadian rhythm adjustment in biology and therapeutic procedures in neuromedicine.