Chaos control by electric current in an enzymatic reaction

Area of Science:

• Biochemical reaction dynamics
• Nonlinear dynamics and chaos theory
• Chemical kinetics

Background:

• The Peroxidase-Oxidase (PO) reaction is a complex biochemical system exhibiting chaotic behavior.
• Controlling chaos in chemical reactions is crucial for understanding and manipulating complex systems.
• Unstable periodic orbits (UPOs) are transient states within chaotic systems that are difficult to stabilize.

Purpose of the Study:

• To apply the continuous delayed feedback method to control chaos in the enzymatic Peroxidase-Oxidase (PO) reaction.
• To stabilize specific unstable periodic orbits (P1, 1(1), and 1(2)) within the PO reaction.
• To demonstrate the effectiveness of electric current as a control parameter for chaos suppression.

Main Methods:

• Utilized Pyragas's continuous delayed feedback method.
• Employed electric current as the control parameter, perturbing platinum electrodes.
• Calculated perturbations based on the difference between delayed and actual signals in the time series.
• Conducted experiments in a continuous stirred tank reactor (CSTR).

Main Results:

• Successfully stabilized unstable periodic orbits (P1, 1(1), and 1(2)) in the PO reaction.
• Demonstrated stabilization through a minimum in the experimental dispersion function.
• Confirmed stabilization by matching the delay time with the period of the stabilized attractor.
• Validated stabilization by showing the embedment of the stabilized periodic attractor within the chaotic attractor.

Conclusions:

• The continuous delayed feedback method is effective for controlling chaos in the enzymatic Peroxidase-Oxidase reaction.
• Electric current perturbations can be used to stabilize specific unstable periodic orbits.
• The study provides a robust method for manipulating complex dynamics in biochemical systems.