How to plot an unstable attractor?
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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 May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
$endgroup$
add a comment
|
6
$begingroup$
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 May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
$endgroup$
1
$begingroup$
Try usingNDSolveinstead
$endgroup$
– b3m2a1
May 26 at 20:55
add a comment
|
6
6
6
1
$begingroup$
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 May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
$endgroup$
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 May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
edited May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
edited May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
edited May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
edited May 27 at 3:56
user64494
4,2162 gold badges14 silver badges23 bronze badges
4,2162 gold badges14 silver badges23 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
asked May 26 at 20:48
JavierJavier
1506 bronze badges
1506 bronze badges
1
$begingroup$
Try usingNDSolveinstead
$endgroup$
– b3m2a1
May 26 at 20:55
add a comment
|
1
$begingroup$
Try usingNDSolveinstead
$endgroup$
– b3m2a1
May 26 at 20:55
1
1
$begingroup$
Try using
NDSolve instead$endgroup$
– b3m2a1
May 26 at 20:55
$begingroup$
Try using
NDSolve instead$endgroup$
– b3m2a1
May 26 at 20:55
add a comment
|
2 Answers
2
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15
$begingroup$
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 May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
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5
$begingroup$
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 May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
15
$begingroup$
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 May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
$endgroup$
add a comment
|
15
$begingroup$
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 May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
$endgroup$
add a comment
|
15
15
15
$begingroup$
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 May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
$endgroup$
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 May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
answered May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
answered May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
answered May 26 at 22:01
Michael E2Michael E2
159k13 gold badges219 silver badges518 bronze badges
159k13 gold badges219 silver badges518 bronze badges
add a comment
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add a comment
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5
$begingroup$
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 May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
$endgroup$
add a comment
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5
$begingroup$
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 May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
$endgroup$
add a comment
|
5
5
5
$begingroup$
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 May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
$endgroup$
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 May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
answered May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
answered May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
answered May 26 at 21:16
b3m2a1b3m2a1
31.7k3 gold badges64 silver badges184 bronze badges
31.7k3 gold badges64 silver badges184 bronze badges
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1
$begingroup$
Try using
NDSolveinstead$endgroup$
– b3m2a1
May 26 at 20:55