Chaos Control by Electric Current in an Enzymatic Reaction

Abstract

We apply the continuous delayed feedback method of Pyragas to control chaos in the enzymatic Peroxidase-Oxidase (PO) reaction, using the electric current as the control parameter. At each data point in the time series, a time delayed feedback function applies a small amplitude perturbation to inert platinum electrodes, which causes redox processes on the surface of the electrodes. These perturbations are calculated as the difference between the previous (time delayed) signal and the actual signal. Unstable periodic P1, 11, and 12 orbits (UPOs) were stabilized in the CSTR (continuous stirred tank reactor) experiments. The stabilization is demonstrated by at least three conditions: A minimum in the experimental dispersion function, the equality of the delay time with the period of the stabilized attractor and the embedment of the stabilized periodic attractor in the chaotic attractor.

Optimal Phase-to-Phase Control of Chemical Oscillations

“…In chemistry, classical engineering techniques (e.g., PID control) were adapted to the needs of control of strongly nonlinear systems. The control of chaotic systems in the Belousov–Zhabotinsky reaction, electrochemical, , enzymatic, and gas-phase systems brought attention to the relationships between nonlinear dynamics and control theory through the recognition of importance of unstable phase state objects (e.g., stationary states and limit cycles). In addition to chaos control, the control of spatiotemporal pattern formation in distributed (e.g., BZ reaction , and CO oxidation) and discrete (e.g., electrochemical reactions on electrode arrays − and BZ beads) systems showed that novel, complex patterns can be obtained by proper application of a feedback signal.…”