{Goodwin oscillator modified from 
Mathematical Biology by J.D. Murray
pg 143
J. Watrous Summer 08}

METHOD RK4
STARTTIME = 0
STOPTIME=50
DT = 0.01

v = 20
k = 1
q = 2
a = 3
b = 4
c = 5
d = 6
r = 7
n = 2

init m = 0.5
init e = 0.1
init p = 0

m' = ((v/(k+(p^q)))-(a*m)) ; mRNA levels

e' = b*m - c*e ; enzyme levels

p' = d*e - r*p ; product levels

{model is unrealistic since large values of q are necessary to show oscillations
a more realistic equation for p would be something like

p' = d*e - (f*p/(k+p))  }

=============================================================

{The Goodwin Oscillator
Adv. Enz. Reg. 3:425-439
J. Watrous Summer 08}

METHOD RK4
STARTTIME = 0
STOPTIME=100
DT = 0.01

a0 = 1
a1 = 72
a2 = 36
k1 = 1
b1 = 2
b2 = 0

init x = 7
init y = -10

{these init values will not yield oscillations
doing parameter plot analysis shows that
values of x between 0.1 and 3 are best and
that y values can varry considerably from there}

x' = (a1/(a2 + (k1 * y))) - b1

y' = a1*x - b2