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Mathematics Equation Solving Wolfram Language

Determine the equilibrium points of a non-linear system

MANIKANDAN R

Posted 5 years ago

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

POSTED BY: MANIKANDAN R

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Bill Nelson

Posted 5 years ago

Try u[x_,y_,z_]:= y; v[x_,y_,z_]:= -dy - UMAXJTanh[k1Sin[x] + k2y + k3z] + d2z - Sin[x]; w[x_,y_,z_]:= dy + UMAXJTanh[k1Sin[x] + k2y + k3z] - d2z + Sin[x] + mu1(UMAXJTanh[k1Sin[x] + k2y + k3z] - d2z); Simplify[w[x,y,z]==0,u[x,y,z]==0&&v[x,y,z]==0] which returns mu1*Sin[x]==0

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