I have a problem: I have the Lotka-Volterra system
y'= y(Cx -E)
and sperimental data (I used some values of the parameters and I solved the system with procedure like "dsolve" of maple or similar).
I would like to find again my parameters starting only to the datas.
I find some book on this problem (Comincioli, Bard) but they say that I should find the explicit function:
x(t)=.... (es. x(t)=Acos(5t)+Be^t -Csin(3t) + D)
and then use the Least Mean Square to find parameters:
Err= 1/2 (explicit x & y depending of A,B,C,E - datas)^2
For this type of ODE, however, it is impossible.
I tried to use Taylor's serie, but it doesn't depend to the parameters.
Now I try to use the energy H (that is a constant in this particular case), but I am not sure that is a good idea: I should use a 5° parameter T:
Err= 1/2 (H(A,B,C,E) - T)^2 and... I don't know T!!!
Someone know this problem and can say me how find information (books, articles, web page...)?
Thank you very much,