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Spontaneous oscillations in two 2-component cells coupled by diffusion.

Journal of Mathematical Biology

|January 1, 1986

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Coupled oscillators exhibit stable oscillations through diffusion, even when individual units do not. This study demonstrates stable oscillations in the Brusselator and glycolytic models using singular perturbation and bifurcation theory.

Area of Science:

Mathematical modeling
Chemical kinetics
Systems biology

Background:

Individual oscillators may not exhibit self-sustained oscillations.
Coupling can induce emergent oscillatory behavior in dynamical systems.
Previous studies often rely on bifurcation theory alone.

Purpose of the Study:

To demonstrate stable oscillations in non-oscillating individual units when coupled.
To apply a novel mathematical approach combining singular perturbation and bifurcation theory.
To analyze the Brusselator and glycolytic oscillation models.

Main Methods:

Mathematical modeling of coupled oscillators.
Application of singular perturbation theory.
Integration with bifurcation analysis.

Related Experiment Videos

Numerical simulations.

Main Results:

For both the Brusselator and glycolytic models, all stationary solutions were shown to be unstable under specific parameter settings.
The existence of stable oscillations (limit cycles) was demonstrated for the Brusselator model within the analyzed parameter range.
The coupling via diffusion was identified as the key mechanism inducing stable oscillations.

Conclusions:

Coupling through diffusion can stabilize oscillations in systems that are otherwise non-oscillatory.
The combined singular perturbation and bifurcation theory approach effectively reveals emergent oscillatory dynamics.
These findings have implications for understanding biological pattern formation and oscillations.