Modelowanie Matematyczne

Ostatnie cwiczenia

ClearAll[μ]

Solve[{μ(x-(x^3)/3)+y==0,-x==0},{x,y}]
{x,y}/.%

D[{μ(x-(x^3)/3)+y,-x},{{x,y}}]
Eigenvalues[%]
%/.{x->0,y->0}
Plot[Abs/@%,{μ,0,5}]

Manipulate[{(1/2) (μ-(Sqrt[-4+(μ^2)])),(1/2) (μ+(Sqrt[-4+(μ^2)]))},{μ,0,5}]

μ=2

Manipulate[
s=NDSolve[{x'[t]==μ(x[t]-((x[t])^3)/3)+y[t],y'[t]==-x[t],x[0]==u[[1]],y[0]==u[[2]]}, {x,y},{t,200}];
GraphicsRow[{Show[ParametricPlot[{x[t],y[t]}/.s,{t,0,200},PlotStyle->Directive[Red,Thick]],VectorPlot[{μ(x-(x^3)/3)+y,-x},{x,-5,5},{y,-5,5},VectorScale->{Automatic,Automatic,None}]],Plot[{x[t],y[t]}/.s,{t,0,50},PlotLegends->SwatchLegend["Expressions",LegendLabel->"label",LegendFunction->(Framed[#,Background->LightBlue]&)]]}],{u,{-5,-5},{5,5}},{{μ,2},0,5},ControlType->{Slider2D,Automatic},ControlPlacement->Left]