Bifurcation diagram

Question

I have a differential equation

y''[t] + 0.3*y'[t] - y[t] + (y[t])^3 == A*Cos[114.14*1.2*t]

with y'[0] == 0, y''[0] == 0

t varies from 0 to 1500, A varies from 0 to 1

How to plot bifurcation diagram (y versus A) of the same?

I tried this code

tab = Table[{sol, points} =  Reap@NDSolveValue[{y''[t] + 0.3*y'[t] - y[t] + (y[t])^3 == 0.3*Cos[114.14*1.2*t], y'[0] == 0, y''[0] == 0}, {y}, {t, 0,1500}];
   {\[Tau], #} & /@ 
    Union[Flatten[points], SameTest -> (Abs[#1 - #2] < .05 &)], {A, 
  0.2, 0.8, .02};
  ListPlot[Flatten[tab, 1]]

But it was not working. Any help and suggestions will be appreciated. Thanks.

Answer 1

You may be looking for something like this,

data = Reap[Do[dsol = 
     NDSolveValue[{y''[t] + 0.3*y'[t] - y[t] + (y[t])^3 == 
        A*Cos[114.14*1.2*t], y''[0] == 0, y'[0] == 0}, 
      y[t], {t, 0, 1500}, MaxStepSize -> 0.01]; 
    Sow[Table[{A, dsol}, {t, 0, 1500}]], {A, 0, 1, 0.01}]][[2, 1]];
ListPlot[data]

Your system looks like a Duffing oscillator and it's always damped within the parameter space you have, i.e. $A\in[0,1]$. Therefore, I think you wouldn't see any bifurcation in your bifurcation diagram.