Stern-Brocot arithmetic in dynamics of a biochemical reaction model

Area of Science:

• Biochemical Reaction Dynamics
• Nonlinear Systems Analysis
• Chemical Kinetics

Background:

• The peroxidase-oxidase reaction is a classic model system in chemical kinetics.
• Previous studies focused on simpler dynamic behaviors.
• A four-variable model exists but its full dynamic repertoire is not well understood.

Purpose of the Study:

• To comprehensively investigate the dynamic behaviors of a 50-year-old four-variable peroxidase-oxidase reaction model.
• To explore nonlinear numerical methods for analyzing complex oscillations and chaos.
• To uncover previously unreported dynamic phenomena within this established model.

Main Methods:

• Utilized 2D isospike stability diagrams.
• Employed 2D maximum Lyapunov exponent diagrams.
• Applied advanced nonlinear numerical simulation techniques.

Main Results:

• Discovered a rich variety of dynamic behaviors for slightly altered parameters.
• Reproduced mixed-mode oscillations, bursting oscillations, and chaotic dynamics.
• Observed mixed-mode oscillations organized by Stern-Brocot arithmetic for specific parameters.
• Identified narrow regions of chaos separating zones of mixed-mode oscillations.

Conclusions:

• The four-variable peroxidase-oxidase model exhibits significantly more complex dynamics than previously recognized.
• Nonlinear analysis reveals unexpected behaviors including organized mixed-mode oscillations and chaos.
• This research expands the understanding of the peroxidase-oxidase reaction's potential for complex system dynamics.