Equilibrium Points of a system of nonlinear equations (Symbolic Solution)

Questions
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1

Hello,

I hope you are doing well.

I am trying to compute equilibrium point of the system below, I typed the equations correctly as the syntax and tried many times but I did not get any solution. The operation ends without any result and the operation last for long.

I did could not figure out, where I did mistake. Can anyone help me with it?

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2

The full symbolic solution may be just hopelessly complicated. I tried with numeric values for the parameters and the solution takes 2.2 MB of memory:

eqs = {\[CapitalLambda] - (Subscript[\[Alpha], 1] B + 
        Subscript[\[Beta], 1]
          D + (Subscript[\[Alpha], 2] + Subscript[\[Beta], 
           2]) C + (Subscript[\[Alpha], 3] + Subscript[\[Beta], 
           3]) P) S - ((Subscript[\[Eta], 1] D + 
           Subscript[\[Eta], 2] C + 
           Subscript[\[Eta], 4] S) B + (Subscript[\[Eta], 3] C + 
           Subscript[\[Eta], 5] P) D) S - \[Mu] S == 
    0, \[Lambda] + (Subscript[\[Alpha], 1] B + 
        Subscript[\[Alpha], 2] C + 
        Subscript[\[Alpha], 3] P) S - (Subscript[\[Rho], 1] D + 
        Subscript[\[Rho], 2] C + Subscript[\[Rho], 3] P + \[Mu] + 
        Subscript[\[Mu], 1] + Subscript[\[Epsilon], 1]) B == 
    0, (Subscript[\[Beta], 1] D + Subscript[\[Beta], 2] C + 
        Subscript[\[Beta], 3] P) S - (\[Mu] + Subscript[\[Mu], 
        1]) D == 
    0, (Subscript[\[Eta], 1]
          D B + (Subscript[\[Eta], 2] B + 
           Subscript[\[Eta], 3] D) C + (Subscript[\[Eta], 4] B + 
           Subscript[\[Eta], 5] D) P) S - (\[Mu] + Subscript[\[Mu], 
        1]) C == 
    0, (Subscript[\[Rho], 1] D + Subscript[\[Rho], 2] C + 
        Subscript[\[Rho], 3] P) B - (\[Mu] + Subscript[\[Mu], 1]) P ==
     0, Subscript[\[Epsilon], 1] B - \[Mu] R == 0};
parameterValues = {Subscript[\[Alpha], 1] -> 1, \[Mu] -> 2, 
   Subscript[\[Beta], 1] -> -1, Subscript[\[Alpha], 2] -> 1, 
   Subscript[\[Beta], 2] -> -2, Subscript[\[Alpha], 3] -> 4, 
   Subscript[\[Beta], 3] -> 3, Subscript[\[Eta], 1] -> 1, 
   Subscript[\[Eta], 2] -> -1, 
   Subscript[\[Eta], 4] -> 1, \[Lambda] -> 1, \[CapitalLambda] -> 1/2,
    Subscript[\[Eta], 3] -> 1, Subscript[\[Eta], 5] -> 2, 
   Subscript[\[Rho], 1] -> 1, Subscript[\[Rho], 2] -> 1, 
   Subscript[\[Rho], 3] -> 1, \[Mu] -> 1, Subscript[\[Mu], 1] -> -1, 
   Subscript[\[Epsilon], 1] -> 2};
Solve[eqs /. parameterValues, Reals]
3

Sir, Thank you very much for the numeric solution, but I need symbolic solution of the system. Actually I tried another system consist of 7 nonlinear equations and I got output, but I stuck in this system of equations. I do not know what mistake I made.

I hope someone will help and point out my mistake.

4

I don’t see any mistakes. The solution may just be too complicated to even write down. What do you need to do with the solution?

5

Sir, the numerical solution is definitely correct but I need equilibrium points of the system symbolically for qualitative analysis of the system.