Hi,
I want to plot a pitchfork bifurcation plot for a DE. I tried with the code as below. It does not show any error but does not show any plot either. I want a plot for x* versus r . Plz advice.
Clear[x];
r=-3;
eqn=x'[t]==r*x[t]+4*x[t]^3;
sol=NDSolve[{eqn,x[0]==0},x,{t,0,100}][[1]];
tTicks=Range[-24,24 30,24];
tGrid=Range[-60,24 30,6];
ParametricPlot[Evaluate[{x[t],x'[t]}/.sol],{t,0,100},
Frame->True,FrameTicks->{tTicks,Automatic},FrameTicksStyle->Directive[Red,Thick],
GridLines->{tGrid,Automatic},GridLinesStyle->LightGray,
FrameLabel->(Style[#,14,Bold]&/@{x,Overscript[x,"."]}),AspectRatio->1]
ParametricPlot[Evaluate[{t,x[t]/.sol}],{t,0,50},Frame->True,FrameTicks->{Range[0,50,12],Automatic},
FrameTicksStyle->Directive[Red,Thick],GridLines->{tGrid,Automatic},GridLinesStyle->LightGray,
FrameLabel->(Style[#,14,Bold]&/@{t,x}),AspectRatio->1]
Sincerely