Modelowanie Matematyczne - laboratoria czwarte, ostatnie :(

Solve[{0==μ(1-(x^2))v-x,0==v},{x,v}]

ReplaceAll[x,Solve[{0==μ(1-(x^2))v-x,0==v},{x,v}]]

m=D[{μ(1-(x^2))v-x,v},{{v,x}}]

Eigenvalues[m]//FullSimplify
Eigenvectors[m]
Eigensystem[m]

{(1/2) (μ-(x^2) μ-(Sqrt[-4-8 v x μ+(((-1+(x^2)))^2) (μ^2)])),(1/2) (μ-(x^2) μ+(Sqrt[-4-8 v x μ+(((-1+(x^2)))^2) (μ^2)]))}/.{x->0,v->0}

Plot[Re/@{(1/2) (μ-(Sqrt[-4+(μ^2)])),(1/2) (μ+(Sqrt[-4+(μ^2)]))},{μ,0,10}]

Block[{μ=2},
StreamPlot[{μ(1-(x^2))v-x,v},{v,-3,3},{x,-3,3},PlotTheme->"Scientific"]]

sol=NDSolve[{v'[t]==2(1-((x[t])^2))v[t]-x[t],x'[t]==v[t],x[0]==1,v[0]==2},{v,x},{t,0,100}];
Plot[Evaluate[{x[t],v[t]}/.sol[[1]]],{t,0,20}]
ParametricPlot[Evaluate[{x[t],v[t]}/.sol[[1]]],{t,0,20}]

Manipulate[
sol=NDSolve[{v'[t]==μ(1-((x[t])^2))v[t]-x[t],x'[t]==v[t],x[0]==u[[2]],v[0]==u[[1]]},{v,x},{t,0,100}];
Show[StreamPlot[{μ(1-(x^2))v-x,v},{v,-4,4},{x,-4,4}],ParametricPlot[Evaluate[{v[t],x[t]}/.sol[[1]]],{t,0,s},PlotStyle->Directive[Black,Thick]]],{{s,10},{5,10,15,20}},{{μ,2},0,5},{u,{-4,-4},{4,4}},ControlType->{Automatic,Automatic,Slider2D},ControlPlacement->Left]
(*,{{s,10},0,100},{{x0,1},-4,4},{{y0,1},-4,4}]]*)