The Computable Differential Equation Lecture ... - Bruce E. Shapiro

146 CHAPTER 7. DELAY DIFFERENTIAL EQUATIONS
Figure 7.2: Numerical integration of y ′ = −y(t − 1), y(t) = 1, −1 < t < 0, on
the interval (0, 10) for three different step sizes using the Forward Euler Method
combined with the Method of Steps.
Next we consider the delay differential equation 1
y ′ (t) =
cy(t − τ)
− λy(t) (7.71)
1 + y(t − τ) m
y(t) = 1, −τ < t < 0 (7.72)
with c = 0.11, λ = 0.21, and m = 10. The only difference in the implementation is
the definition of the function f[t]:
f[t ] := Module[{
λ = 0.11, c = 0.21, m = 10, i, ydelay, ynow, v},
i = index[t - tau, tau, n];
ydelay = data[[i]];
ynow = Last[data];
v = c*ydelay/(1 + ydelay m ) - λ*ynow;
Return[v];
];
This function makes the assumption that whenever f[t] is called the current value
of y(t) is stored the last element of the list array data. In the illustrations shown
in figure 7.3 we have also modified the call to ListPlot to also display the value of
tau,
1 This equation is derived from a model of respiration, M.C.Mackey and L.Glass (1977) “Oscillation
and chaos in physiological control systems,” Science, 197:287-289.
Math 582B, Spring 2007
California State University Northridge
c○2007, B.E.Shapiro
Last revised: May 23, 2007