Glycolytic Oscillations: The Higgins-Selkov Model
by Mike Martin

On this page, solutions curves (both in time and phase) are generated for the Higgins-Selkov model of glycolytic oscillations. The equations are of the form:

S ' (t) = vo - k1 (P (t))2 S (t)

P ' (t) = k1 (P (t))2 S (t) - k2 P (t)

S (0) = So
P (0) = Po

The user inputs values of the parameters vo, k1, and k2. Also, gird bounds, time bounds, and the initial conditions must be specified. The solution to this IVP is solved using Mathematica's NDSolve package. The small black point in the phase plane and red points in the x, & y plots indicate the initial condition positions.



Enter in the value of the parameters and select the plotting bounds, then press the "Plot/Evaluate" button.

vo =  

k1 =  

k2 =  


S (0) =  

P (0) =  


0   ≤   t   ≤  


  ≤   S   ≤  

  ≤   P   ≤  


References:

Wikipedia's Phase Portrait

MathWorld's Phase Portrait

DFIELD & PPLANE -- web utilities

Community of Ordinary Differential Equations Educators