  A simplified model for the complex glycolytic process was historically
proposed by Selkov. It showed the existence of stable limit cycle as an example
of Poincare-Bendixson theorem. This limit cycle is nothing but the time
eliminated Lissajous plot of the concentrations of Adenosine-diphosphate (ADP)
and Fructose-6-phosphate (F6P) of a normal/healthy human. Deviation from this
limit cycle is equivalent to the deviation of normal physiological behaviour.
It is very important to know how long a human body will take to reach the
glycolytic stable limit cycle, if deviated from it. However, till now the
convergence time, depending upon different initial parameter values, was not
studied in detail. This may have great importance in understanding the recovery
time for a diseased individual deviated from normal cycle. Here the convergence
time for different initial conditions has been calculated in original Selkov
model. It is observed that convergence time, as a function of the distance from
the limit cycle, gets saturated away from the cycle. This result seems to be a
physiological disorder. A possible mathematical way to incorporate this in the
Selkov model, has been proposed.
