How to plot an unstable attractor?Why does DSolve return two solutions for my ODE?Second Order ODE (Bessel Function) with a dependent variable in the BCDSolve doesn't give all the solutionsUsing DSolve for a coupled differential equationDSolve not satisfying initial conditionshow to To specify initial conditions for a system of ode?DAE with NDSolve -monitor numerical noiseDSolve - Unable to obtain plot of solution - 2nd order ODEPartial differential equation heat/diffusion equation 3dCannot solve ODE question with Initial Value
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How to plot an unstable attractor?
Why does DSolve return two solutions for my ODE?Second Order ODE (Bessel Function) with a dependent variable in the BCDSolve doesn't give all the solutionsUsing DSolve for a coupled differential equationDSolve not satisfying initial conditionshow to To specify initial conditions for a system of ode?DAE with NDSolve -monitor numerical noiseDSolve - Unable to obtain plot of solution - 2nd order ODEPartial differential equation heat/diffusion equation 3dCannot solve ODE question with Initial Value
$begingroup$
I'm trying to solve and plot the following in Mathematica:
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
DSolve[eqns, x, y, t]
This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.
plotting differential-equations
edited 1 hour ago
user64494
3,88711323
asked 8 hours ago
JavierJavier
1305
$endgroup$
add a comment |
$begingroup$
I'm trying to solve and plot the following in Mathematica:
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
DSolve[eqns, x, y, t]
This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.
plotting differential-equations
edited 1 hour ago
user64494
3,88711323
asked 8 hours ago
JavierJavier
1305
$endgroup$
$begingroup$
Try usingNDSolveinstead
$endgroup$
– b3m2a1
8 hours ago
add a comment |
$begingroup$
I'm trying to solve and plot the following in Mathematica:
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
DSolve[eqns, x, y, t]
This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.
plotting differential-equations
edited 1 hour ago
user64494
3,88711323
asked 8 hours ago
JavierJavier
1305
$endgroup$
I'm trying to solve and plot the following in Mathematica:
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
DSolve[eqns, x, y, t]
This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.
plotting differential-equations
plotting differential-equations
edited 1 hour ago
user64494
3,88711323
asked 8 hours ago
JavierJavier
1305
edited 1 hour ago
user64494
3,88711323
asked 8 hours ago
JavierJavier
1305
edited 1 hour ago
user64494
3,88711323
edited 1 hour ago
user64494
3,88711323
edited 1 hour ago
user64494
3,88711323
3,88711323
asked 8 hours ago
JavierJavier
1305
asked 8 hours ago
JavierJavier
1305
asked 8 hours ago
JavierJavier
1305
1305
$begingroup$
Try usingNDSolveinstead
$endgroup$
– b3m2a1
8 hours ago
add a comment |
$begingroup$
Try usingNDSolveinstead
$endgroup$
– b3m2a1
8 hours ago
$begingroup$
Try using
NDSolve instead$endgroup$
– b3m2a1
8 hours ago
$begingroup$
Try using
NDSolve instead$endgroup$
– b3m2a1
8 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
To visualize a 2D system, I would start with StreamPlot:
vf = x', y' /. First@Solve[eqns /. f_[t] :> f, x', y']; (* strip the args *)
StreamPlot[vf, x, -2, 2, y, -2, 2]
You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:
ics = Cos[1/5], Sin[1/5], Red,
0.5, 0, Magenta, 1.5, 0., Magenta;
StreamPlot[vf, x, -2, 2, y, -2, 2,
StreamPoints -> Append[ics, Automatic],
Epilog -> White, EdgeForm[Black], Disk[1, 0, 0.03]]
answered 7 hours ago
Michael E2Michael E2
153k12208493
$endgroup$
$begingroup$
this was what I was looking for
$endgroup$
– Javier
7 hours ago
add a comment |
$begingroup$
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
sol = NDSolve[Join[x[0]==1.5, y[0]==1.5, eqns], x, y, t, 0, 50];
ParametricPlot[x[t], y[t]/.sol//Evaluate, t, 0, 50, PlotRange->All]
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
$endgroup$
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
To visualize a 2D system, I would start with StreamPlot:
vf = x', y' /. First@Solve[eqns /. f_[t] :> f, x', y']; (* strip the args *)
StreamPlot[vf, x, -2, 2, y, -2, 2]
You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:
ics = Cos[1/5], Sin[1/5], Red,
0.5, 0, Magenta, 1.5, 0., Magenta;
StreamPlot[vf, x, -2, 2, y, -2, 2,
StreamPoints -> Append[ics, Automatic],
Epilog -> White, EdgeForm[Black], Disk[1, 0, 0.03]]
answered 7 hours ago
Michael E2Michael E2
153k12208493
$endgroup$
$begingroup$
this was what I was looking for
$endgroup$
– Javier
7 hours ago
add a comment |
$begingroup$
To visualize a 2D system, I would start with StreamPlot:
vf = x', y' /. First@Solve[eqns /. f_[t] :> f, x', y']; (* strip the args *)
StreamPlot[vf, x, -2, 2, y, -2, 2]
You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:
ics = Cos[1/5], Sin[1/5], Red,
0.5, 0, Magenta, 1.5, 0., Magenta;
StreamPlot[vf, x, -2, 2, y, -2, 2,
StreamPoints -> Append[ics, Automatic],
Epilog -> White, EdgeForm[Black], Disk[1, 0, 0.03]]
answered 7 hours ago
Michael E2Michael E2
153k12208493
$endgroup$
$begingroup$
this was what I was looking for
$endgroup$
– Javier
7 hours ago
add a comment |
$begingroup$
To visualize a 2D system, I would start with StreamPlot:
vf = x', y' /. First@Solve[eqns /. f_[t] :> f, x', y']; (* strip the args *)
StreamPlot[vf, x, -2, 2, y, -2, 2]
You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:
ics = Cos[1/5], Sin[1/5], Red,
0.5, 0, Magenta, 1.5, 0., Magenta;
StreamPlot[vf, x, -2, 2, y, -2, 2,
StreamPoints -> Append[ics, Automatic],
Epilog -> White, EdgeForm[Black], Disk[1, 0, 0.03]]
answered 7 hours ago
Michael E2Michael E2
153k12208493
$endgroup$
To visualize a 2D system, I would start with StreamPlot:
vf = x', y' /. First@Solve[eqns /. f_[t] :> f, x', y']; (* strip the args *)
StreamPlot[vf, x, -2, 2, y, -2, 2]
You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:
ics = Cos[1/5], Sin[1/5], Red,
0.5, 0, Magenta, 1.5, 0., Magenta;
StreamPlot[vf, x, -2, 2, y, -2, 2,
StreamPoints -> Append[ics, Automatic],
Epilog -> White, EdgeForm[Black], Disk[1, 0, 0.03]]
answered 7 hours ago
Michael E2Michael E2
153k12208493
answered 7 hours ago
Michael E2Michael E2
153k12208493
answered 7 hours ago
Michael E2Michael E2
153k12208493
answered 7 hours ago
Michael E2Michael E2
153k12208493
153k12208493
$begingroup$
this was what I was looking for
$endgroup$
– Javier
7 hours ago
add a comment |
$begingroup$
this was what I was looking for
$endgroup$
– Javier
7 hours ago
$begingroup$
this was what I was looking for
$endgroup$
– Javier
7 hours ago
$begingroup$
this was what I was looking for
$endgroup$
– Javier
7 hours ago
add a comment |
$begingroup$
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
sol = NDSolve[Join[x[0]==1.5, y[0]==1.5, eqns], x, y, t, 0, 50];
ParametricPlot[x[t], y[t]/.sol//Evaluate, t, 0, 50, PlotRange->All]
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
$endgroup$
add a comment |
$begingroup$
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
sol = NDSolve[Join[x[0]==1.5, y[0]==1.5, eqns], x, y, t, 0, 50];
ParametricPlot[x[t], y[t]/.sol//Evaluate, t, 0, 50, PlotRange->All]
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
$endgroup$
add a comment |
$begingroup$
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
sol = NDSolve[Join[x[0]==1.5, y[0]==1.5, eqns], x, y, t, 0, 50];
ParametricPlot[x[t], y[t]/.sol//Evaluate, t, 0, 50, PlotRange->All]
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
$endgroup$
eqns = x'[t] ==
x[t] - y[t] -
x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2],
y'[t] ==
x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) -
x[t]^2/Sqrt[x[t]^2 + y[t]^2];
sol = NDSolve[Join[x[0]==1.5, y[0]==1.5, eqns], x, y, t, 0, 50];
ParametricPlot[x[t], y[t]/.sol//Evaluate, t, 0, 50, PlotRange->All]
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
answered 8 hours ago
b3m2a1b3m2a1
29.9k360176
29.9k360176
add a comment |
add a comment |
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$begingroup$
Try using
NDSolveinstead$endgroup$
– b3m2a1
8 hours ago