Modelowanie matematyczne

Zajecia  4. 
13.03 2018

Solve

Solve[μ(x-(x^3)/3)+y==0&&-x==0,{x,y}]

D[{5x+3y,y-x},{{x,y}}]

D[{μ(x-(x^3)/3)+y,-x},{{x,y}}]

Eigenvalues[{{(1-(x^2)) μ,1},{-1,0}}]/.{x->0,y->0}
Plot[Evaluate[Re/@%],{μ,0,5}]

Plot[Evaluate[Re/@Eigenvalues[{{(1-(x^2)) μ,1},{-1,0}}]/.{x->0,y->0}],{μ,0,5}]

StreamPlot

StreamPlot[{2(x-(x^3)/3)+y,-x},{x,-3,3},{y,-3,3},VectorPoints->15,VectorStyle->Red]

Manipulate[s=NDSolve[{x'[t]==μ(x[t]-(((x[t]))^3)/3)+y[t],y'[t]==-x[t],x[0]==x0,y[0]==y0},{x,y},{t,0,30}] ;
GraphicsGrid[{{Plot[Evaluate[{x[t],y[t]}/.s],{t,0,tx},PlotStyle->Thick],
Show[StreamPlot[{μ(x-(x^3)/3)+y,-x},{x,-3,3},{y,-3,3},VectorPoints->15,VectorStyle->Red,Epilog->{Green,Disk[{x0,y0},0.25]}],
ParametricPlot[Evaluate[{x[t],y[t]}/.s],{t,0,tx},PlotStyle->Thick]

]
}}],{tx,1,30},{{x0,2},-3,3},{{y0,3},-3,3},{{μ,2},0,5}]