I am trying to simulate the behaviour of an equation in the continuous domain for two different populations given a set of parameters.
The equations reads:
S(t) = exp(-alpha·D(t)-beta·G·D^2(t))
where alpha and beta are known (and are different for two populations of cells), and G may be:
Case 1: G=1
Case 2: G = (D1^2+D2^2+2*D1*D2*exp(-lambda*T))/D^2 (where D1=D/3; D2=2·D/3; and lambda is also known)
For the Case 1, I need to simulate for different values of D. Even if for the purposes of this case, D(t) = D0 (a constant); I would like to know how I would do it for a time-dependent D, for example, D(t) = D0·t, with a varying D0, for example in the range [1..8].
For the Case 2, I need to simulate under different values of T (for example in the range [1..8]), letting D be a constant, known value. In this case, D(t) is a piecewise function:
= D/3 if t=0
= 2·D/3 if t=T
= 0 for any other t
I really don't know how to write the expression for S(t) in this case.
I guess I need an array to store as many instances of S as numbers of parameters I have (8 values for D0 int he first case, and another eight for T).
And besides, it needs to be a function of t (even if in the first case, it is not; I'd like to simulate as if it were).
So I am at a loss when it comes to writing the expressions of S(t), and having it evaluated (and its values plot in the same graph using a palette for differente parameter values) for say, t=0..100.
Attached is my attempt: Mapleprimes_LQ_model_simulation.mw