Hopf Bifurcation in the Sel'kov Model

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This Demonstration allows interactive manipulation of the Sel'kov model for glycolysis—an important metabolic pathway in which glucose is broken down to make pyruvate. The model exhibits a Hopf bifurcation as the key parameter is varied, resulting in the appearance of a stable limit cycle. Glycolytic oscillations are seen in real biological systems.

Contributed by: Jeremy Owen (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The Sel'kov model is a two-dimensional system of differential equations:

,

.

Snapshot 1: a solution trajectory that settles on the stable limit cycle

Snapshot 2: a solution trajectory that comes to a stable equilibrium

Snapshot 3: a solution trajectory that spirals out from within a limit cycle



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