Get a simple form of an equilibrium point of a nonlinear ODEs system?

Posted 15 days ago
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 Dear all, I am a beginner user of Mathematica Software. I used nonlinear ODEs system and get enumerate result how to put the results in a simple form. f[T_, I1_] = \[Alpha]1 T (1 - \[Alpha]2 T) - \[Alpha]4 T I1; g[T_, I1_] = \[Sigma] - \[Delta] I1 - \[Mu]2 T I1 + (\[Rho]2 T I1)/( m2 + T) ; s = Solve[{f[T, I1] == 0, g[T, I1] == 0}, {T, I1}]; Simplify[s, {m2 > 0, \[Alpha]1 > 0, \[Alpha]2 > 0, \[Alpha]4 > 0, \[Delta] > 0, \[Mu]2 > 0, \[Rho]2 > 0, \[Sigma] > 0}] the result is still complicated and I can't determine the sign of points. The points should to be positive and reals. However, I want to do a simulation of the model by Mathematica. can do it?
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Posted 14 days ago
 You can display the solutions in the complex plane: With[{s = s}, Manipulate[ Graphics[{PointSize[Large], Point[ReIm[T]], Red, Point[ReIm[I1]]} /. s, Frame -> True], {{m2, 1/2}, 0, 1}, {{\[Alpha]1, 1/2}, 0, 1}, {{\[Alpha]2, 1/2}, 0, 1}, {{\[Alpha]4, 1/2}, 0, 1}, {{\[Delta], 1/2}, 0, 1}, {{\[Mu]2, 1/2}, 0, 1}, {{\[Rho]2, 1/2}, 0, 1}, {{\[Sigma], 1/2}, 0, 1}]] 
Posted 14 days ago
 how this code is help me to solve my problem. I want to find the simplest result of the steady-state. if you do run the model you can see how it is enormous. this is my problem.
Posted 14 days ago
 You have 4 solutions. You need to choose the ones that are real and positive. This plot visualizes the solutions in the complex plane, so that you can choose: With[{s = s}, Manipulate[ Graphics[{PointSize[ Large], {Dashed, Point[ReIm[T]], Text["T", ReIm[T], {0, -2}], Red, Point[ReIm[I1]], Text["I1", ReIm[I1], {0, -2}]} /. s[[i]]}, Frame -> True, PlotRangePadding -> Scaled[.1]], {i, {1, 2, 3, 4}}, {{m2, 1/2}, 0, 1}, {{\[Alpha]1, 1/2}, 0, 1}, {{\[Alpha]2, 1/2}, 0, 1}, {{\[Alpha]4, 1/2}, 0, 1}, {{\[Delta], 1/2}, 0, 1}, {{\[Mu]2, 1/2}, 0, 1}, {{\[Rho]2, 1/2}, 0, 1}, {{\[Sigma], 1/2}, 0, 1}]] Solution number 1 has T=0, is that acceptable?
Posted 13 days ago
 yes on of them is T=0, there is two points are complex the fourth is real but i can't determine its sign.