Determine the equilibrium points of a non-linear system

Questions
1

Hi I am trying to determine the equilibrium points in terms of the nondimensional parameters. the following is the non dimensionalised system:

equation.PNG
equation.PNG729×184 10.7 KB

mate.PNG
mate.PNG1230×222 9.36 KB

2

Please post code in copy-pastable format.

3

Si thanks, Please find

u[x, y, z] := y;

v[x, y, z] := (-d*
     y) - (UMAXJ*(tanh[k_ 1*sin[x] + k_ 2*y + k_ 3*z])) + (d_ 2*
     z) - (sin[x]);

w[x, y, z] := (d*y) + (UMAXJ*(tanh[k_ 1*sin[x] + k_ 2*y + k_ 3*z]) - 
     d_ 2*z) + (mu1*((UMAXJ*tanh[k_ 1*sin[x] + k_ 2*y + k_ 3*z]) - 
       d_ 2*z)) + (sin[x]);

sols = NSolve[{u[x, y, z] == 0, v[x, y, z] == 0, w[x, y, z] == 0}, {u,
     v, w}, Reals];
4

Sir, Herein Mathematica file attached

my.nb (4.83 KB)

5

Try

u[x_,y_,z_]:= y;
v[x_,y_,z_]:= -d*y - UMAXJ*Tanh[k1*Sin[x] + k2*y + k3*z] + d2*z - Sin[x];
w[x_,y_,z_]:=  d*y + UMAXJ*Tanh[k1*Sin[x] + k2*y + k3*z] - d2*z + Sin[x] +
                mu1*(UMAXJ*Tanh[k1*Sin[x] + k2*y + k3*z] - d2*z);
Simplify[w[x,y,z]==0,u[x,y,z]==0&&v[x,y,z]==0]

which returns

mu1*Sin[x]==0
6

Thanks