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Selection between multiple periodic regimes in a biochemical system: complex dynamic behaviour resolved by use of
Journal of Theoretical Biology
|April 21, 1985
Summary
This study analyzes coupled enzyme reactions, revealing how initial conditions determine outcomes in systems with multiple stable states (birhythmicity). Fractal basin boundaries lead to unpredictable behavior, termed final state sensitivity.
Area of Science:
- Biochemistry
- Chemical Kinetics
- Systems Biology
Background:
- Autocatalytic enzyme reactions are fundamental to many biological processes.
- Coupled reactions can exhibit complex dynamics, including multiple stable periodic regimes.
- Understanding the influence of initial conditions is crucial for predicting system behavior.
Purpose of the Study:
- To analyze a model biochemical system with two coupled autocatalytic enzyme reactions.
- To determine how different initial conditions lead to distinct periodic regimes.
- To investigate the phenomenon of final state sensitivity arising from fractal basin boundaries.
Main Methods:
- Analysis of a model biochemical system with coupled autocatalytic enzyme reactions.
- Determination of attraction basin structures for coexisting limit cycles (birhythmicity).
- Derivation of one-dimensional return maps from time evolution and polynomial equations.
Main Results:
- Identified conditions where multiple stable periodic regimes coexist.
- Demonstrated that attraction basin structures can be simple or highly complex, especially with fractal boundaries.
- Explained complex phenomena like final state sensitivity using one-dimensional return maps.
Conclusions:
- The study provides a unified explanation for complex dynamics in birhythmic systems.
- Enhanced sensitivity to initial conditions can arise from fractal basin boundaries.
- Suggests experimental tests for birhythmic chemical systems and discusses physiological significance for biological rhythms.