Originally Posted by

**laureanda** Hello,

I have a problem: I have the Lotka-Volterra system

x'= x(A-By)

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)

y(t)=....

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,

Ilaria