Hi guys,
I want to calculate the steady states of a system of differential equations:
from sympy import *
X,Y,Z = symbols("X,Y,Z")
variables_dimless = [X,Y,Z]
Rxy,Rxz, Ry,Ryx,Ryz, Rz,Rzy,Rzz = symbols("Rxy,Rxz, Ry,Ryx,Ryz,
Rz,Rzy,Rzz",positive=True)
dimensionless_DES_list = [X*(1-X),
Ry *(Y* (1 - Y) + Rzy * Z *Y ),
Rz *(Z*(1-Z)+Rxz*X*Z+Ryz*Y*Z)]
equilibria = solve( dimensionless_DES_list,(variables_dimless))
Out[2]:
[(0, 0, 0),
(0, 0, 1),
(0, 1, 0),
(0, -(Rzy + 1)/(Ryz*Rzy - 1), -(Ryz + 1)/(Ryz*Rzy - 1)),
(1, 0, 0),
(1, 0, Rxz + 1),
(1, 1, 0),
(1, -(Rxz*Rzy + Rzy + 1)/(Ryz*Rzy - 1), -(Rxz + Ryz + 1)/(Ryz*Rzy - 1
))]
My problem are the negative signs of the results for example solution 4:
(0, -(Rzy + 1)/(Ryz*Rzy - 1), -(Ryz + 1)/(Ryz*Rzy - 1)),
For future calculation it is important that all solutions of the variables
have a positive sign. The solution should look like:
(0, (Rzy + 1)/(1 - Ryz*Rzy), (Ryz + 1)/(1 - Ryz*Rzy )),
I do not know how to manipulate the output. If I define the variables as
following
X,Y,Z = symbols("X,Y,Z",positive=True)
The solver just finds the one solution were X,Y,Z are positive.
Do you have any ideas?
Thank you in advance
Alex
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