Mathematica modelling question

[senan]

I'm kinda of messing around with a model of a biological system, I've found the equilibriums and decided I'd get the stability relations as well. I tried using mathematica to get the eigenvalues of the system to see if its stable or not and when I got the eigenvalues of my matrix mathematica kicked this back at me.


Root[a^2 *b^2*d*e^2 *m + 2 *a^3 *b *d*e *t *m + a^4 *d *t^2 *m + a*b^3 *g *d
*e *r+ a^2*b^2 *g*d*t*r + (a^2 *b^2d*e^2*m +a*b^2*e^3 *m + a^3 *b*d*e*t*m + 3a^2 *b*e^2*t*m +
2a^3 *e*t^2*m + a*b^3g*d*e*r) #1 + (b^3 *e^3*r +a*b^2 *e^2 *t*r) #1^2 + b^3*e^3*r #1^3 &, 1]

i know the # marks mean to input the function at address 1 in this case but seeing as i got the eigenvalues of a 3x3 matrix what would that be in this case

 

[CompuChip]

Basically it tries to tell you that the answer you are looking for is the solution of f(x) = 0 for some complicated f(x), but that it cannot solve that expression for x.

 

[Bill Simpson]

Sometimes, but not always it is possible to get the explicit form of a Root object in terms of radicals.

To do this wrap a ToRadicals[] around your Root object and in this example MMA can find it, but the result is more than triple the size. Simplify[] on that can reduce it down to something a little more than double the original size.

 

[senan]

Thanks for ye're replies. I think I'm going to have to go back and try and simplify th system a bit it. Hopefully I can reduce it down further by adjusting a few terms

 

[blue_raver22]

It seems like you are trying to use Mathematica to calculate the eigenvalues of a biological system. The output you received is in the form of a root function, which represents the roots of a polynomial equation. In this case, the # marks indicate that the function is dependent on the value of the input, which is 1 in this case. This is because the eigenvalues of a matrix are calculated by solving the characteristic equation, which is a polynomial equation. Therefore, the output you received is the roots of the characteristic equation for your system. In order to determine the stability of your system, you can use the eigenvalues to calculate the stability relations, as you mentioned. I suggest consulting with a mathematician or a biologist to confirm the accuracy of your model and to assist you in interpreting the results.