Hopf Bifurcation in the Sel'kov Model
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.
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