Message Boards

WOLFRAM COMMUNITY

4880 Views

2 Replies

2 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

How to plot Pitchfork bifuration curve for a nonlinear DE?

Rahul Chakrabory

Posted 9 years ago

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]==rx[t]+4x[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

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

POSTED BY: Rahul Chakrabory

2 Replies

Sort By:

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 9 years ago

Maybe you want something like this: StreamDensityPlot[{0, r x + x^3}, {r, -3, 3}, {x, -2, 2}, ColorFunctionScaling -> False, ColorFunction -> "TemperatureMap"] which gives: Regards -- Henrik

POSTED BY: Henrik Schachner

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 9 years ago

I think you're solution is 0 everywhere. In[23]:= r = -3; eqn = x'[t] == rx[t] + 4x[t]^3; sol = DSolve[{eqn, x[0] == 0}, x, {t, 0, 100}] During evaluation of In[23]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >> During evaluation of In[23]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >> Out[25]= {{x -> Function[{t}, 0]}}

I think you're solution is 0 everywhere.

In[23]:= r = -3;
eqn = x'[t] == r*x[t] + 4*x[t]^3;
sol = DSolve[{eqn, x[0] == 0}, x, {t, 0, 100}]

During evaluation of In[23]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

During evaluation of In[23]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

Out[25]= {{x -> Function[{t}, 0]}}

POSTED BY: Frank Kampas

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Group Abstract

Feedback