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I have a coupled system of equations which depend on time explicitly. for example:
x'[t] = x[t]* Cos[bt] - y[t]^2/(1-y[t])^2 ,
y'[t] = Cos[a
t] * y[t] * Cos[x[t]]

I want to plot the phase portrait or poincare section of this system of equations; but I only found the answer in systems that are time independent. I tried ParametricPlot but it doesn't seem to work.

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    $\begingroup$ What is known about a,b? $\endgroup$ Commented Jun 25, 2023 at 16:48
  • $\begingroup$ We know their values for example b= 0.25 , a = 0.15 $\endgroup$
    – melika
    Commented Jun 26, 2023 at 17:10

1 Answer 1

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You might try numerical solution:

a = .15;
b = .25;
tsim = 150;
{X, Y} = NDSolveValue[{
x'[t] == x[t] Cos[b t] - (y[t] /(1 - y[t]))^2, 
y'[t] == Cos[a t] y[t] Cos[x[t]]
, x[0] == 1/10, y[0] == 1/10}
, {x,y}, {t, 0, tsim}]


ParametricPlot[{X[t] , Y[t]}, {t, 0, 100} ,PlotRange -> {{-500, 0}, {0, 1}}, AspectRatio -> 1]

enter image description here

But solution doesn't look promising! Check the ode's.

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