Phase Portrait of Van der pol Oscillator with pgfplots

Question

I'm sorry for not providing code for my question, as I usually always provide code but this time I am not really sure how to achieve my goal, which is why I would like your guy's help. So I am trying to plot the phase Portrait of a van der pol oscillator. The way I wish the plot to look is this way:

I am trying to emphasize the attraction region. My problem is the followong:

1) I am not familiar with quiver and also not sure how to use it

2) I can get the data from Matlab but I do not know how to use it

A code example of how this can be achieved would of course be perfect but tips on how to use tikz in combination with Matlab would also be okay. Till now I exported a data set with the command stated in pgfplots with 4 columns (x,y,u,v) but I am not really sure how to use them. Is there a way to make pgf use the ready data ?

I appreciate all the help

   5.0000000e+00   5.0000000e+00   1.5375045e-02  -3.8620859e-01
   5.0153750e+00   4.6137914e+00   3.4876123e-02  -8.9247723e-01
   5.0697522e+00   3.2150455e+00   4.7120884e-02  -1.2339311e+00
   5.1096168e+00   2.1459291e+00   3.2612691e-02  -8.9119732e-01
   5.1349776e+00   1.4326509e+00   2.0692523e-02  -5.9536377e-01
   5.1510019e+00   9.5520159e-01   1.3088303e-02  -4.0194104e-01
   5.1611542e+00   6.2876881e-01   8.2438303e-03  -2.7656489e-01
   5.1674895e+00   4.0207181e-01   5.0626974e-03  -1.9276422e-01
   5.1712796e+00   2.4324037e-01   2.9348841e-03  -1.3523094e-01
   5.1733593e+00   1.3160992e-01   1.5130955e-03  -9.4896595e-02
   5.1743058e+00   5.3447176e-02   5.8677480e-04  -6.1018779e-02
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  -2.0083067e+00   1.2050706e-01   6.8649971e-03   9.9618557e-02
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  -5.0009333e-01   1.6458678e+00   3.4815941e-01   3.6122922e-01
  -1.2919459e-01   2.0409216e+00   3.2602662e-01   3.3665136e-01
   1.5195992e-01   2.3191705e+00   2.9838308e-01   2.6066088e-01
   4.6757156e-01   2.5622433e+00   3.0601859e-01   1.7770385e-01
   7.6399710e-01   2.6745782e+00   2.9247767e-01   3.0969255e-02
   1.0525269e+00   2.6241818e+00   2.9128230e-01  -1.6186784e-01
   1.3465617e+00   2.3508425e+00   2.4601433e-01  -3.1068418e-01
   1.5445556e+00   2.0028135e+00   1.8044909e-01  -3.8204061e-01
   1.7074599e+00   1.5867613e+00   1.4017150e-01  -4.0752963e-01
   1.8248986e+00   1.1877542e+00   1.0140544e-01  -3.8573509e-01
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   1.9706183e+00   4.6339070e-01   4.8189777e-02  -3.6427720e-01
   2.0066503e+00   8.6736710e-02   1.8659083e-02  -2.5250145e-01
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   7.1897052e-01  -1.4211293e+00  -3.2260991e-01  -3.1949462e-01
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  -1.7720148e-02  -2.1907966e+00  -3.2545170e-01  -3.2153939e-01
  -2.9145058e-01  -2.4383333e+00  -2.8694493e-01  -2.1743893e-01
  -5.9161002e-01  -2.6256744e+00  -2.9488168e-01  -1.1876703e-01
  -8.8121394e-01  -2.6758673e+00  -2.9212345e-01   4.2654315e-02
  -1.1758569e+00  -2.5403658e+00  -2.8958294e-01   2.5354649e-01
  -1.4603798e+00  -2.1687743e+00  -2.4488695e-01   4.1728897e-01
  -1.6656308e+00  -1.7057879e+00  -1.4133867e-01   3.4676055e-01
  -1.7430571e+00  -1.4752532e+00  -7.7426317e-02   2.3053465e-01

Edit: I added some data that I've accumulated from MATLAB simulations.

The matlab plot looks like this: []

The columns are 1: x 2:y 3:u 4: v

Answer 1

The Van der Pol Oscillator can be represented as:

$$ \dot{x}=y, \dot{y}=\mu (1-x^2)y-x $$

Simulating this system in Matlab, from different initial conditions and $\mu=0.8$, we will get trajectories that converge to a stable limit cycle.

To draw this in LaTeX, we can use Pgfplots package. We distinguish two parts:

1. Trajectories and the limit cycle: We can export data from matlab and plot it using \addplot[options] file{filename.txt}
2. Vector field: based on the system dynamics, we can draw the phase portrait using quiver with \addplot3

Here is the corresponding code:

\documentclass[border=0.2cm]{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat = newest}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    xmin = -4, xmax = 4,
    ymin = -4, ymax = 4,
    width = \textwidth,
    height = 0.7\textwidth,
    xlabel = {$x$},
    ylabel = {$y$},
    view = {0}{90},
    colormap/viridis,
    ]

\addplot3[
    point meta = {sqrt(x^2+y^2)},
    quiver = {
        u = {y/sqrt(y^2+(0.8*(1-x^2)*y-x)^2)},
        v = {(0.8*(1-x^2)*y-x)/sqrt(y^2+(0.8*(1-x^2)*y-x)^2)},
        scale arrows = 0.25,
        },
    quiver/colored = {mapped color},
    -stealth,
    domain = -4:4,
    domain y = -4:4,
    ] {0};


\addplot[very thick, red] file {data.txt};

\end{axis}
\end{tikzpicture}

\end{document}

data.txt contains your data obtained from Matlatb (x and y trajectories). In this case, it corresponds to the limit cycle (steady state trajectory). After simulation, you can extract steady state data to get only the limit cycle part and not the transient.

-1.4524 -2.0041
-1.5484 -1.8329
-1.6354 -1.6464
-1.7128 -1.4509
-1.7804 -1.2526
-1.8381 -1.0571
-1.8863 -0.86899
-1.9252 -0.69163
-1.9556 -0.52729
-1.9782 -0.37716
-1.9936 -0.24155
-2.0026 -0.12011
-2.0058 -0.012026
-2.004 0.083793
-1.9976 0.16859
-1.9873 0.24366
-1.9734 0.31025
-1.9564 0.36955
-1.9366 0.42265
-1.9142 0.47053
-1.8896 0.51406
-1.8629 0.55402
-1.8342 0.59108
-1.8038 0.62583
-1.7717 0.65879
-1.738 0.69041
-1.7027 0.72111
-1.6659 0.75124
-1.6275 0.78112
-1.5877 0.81105
-1.5464 0.8413
-1.5036 0.87212
-1.4592 0.90377
-1.4132 0.93647
-1.3655 0.97046
-1.3161 1.006
-1.2649 1.0432
-1.2118 1.0825
-1.1566 1.1239
-1.0994 1.1678
-1.0398 1.2144
-0.97786 1.264
-0.91335 1.3167
-0.84613 1.3729
-0.77601 1.4326
-0.7028 1.4961
-0.62633 1.5635
-0.54639 1.6348
-0.46279 1.7098
-0.37535 1.7884
-0.2839 1.8701
-0.18831 1.954
-0.088478 2.0392
0.015613 2.1242
0.1239 2.2068
0.23622 2.2847
0.35224 2.3547
0.4715 2.4132
0.59331 2.4563
0.7168 2.4798
0.8409 2.4798
0.96433 2.4528
1.0857 2.3965
1.2035 2.3099
1.3162 2.1938
1.4224 2.0509
1.5209 1.8853
1.6106 1.7027
1.691 1.5093
1.7615 1.3112
1.8221 1.1144
1.873 0.92364
1.9146 0.7428
1.9475 0.57444
1.9723 0.42004
1.9897 0.28015
2.0005 0.15459
2.0054 0.042661
2.005 -0.05666
2 -0.14459
1.9907 -0.2224
1.9779 -0.29137
1.9617 -0.35271
1.9427 -0.40753
1.9211 -0.45686
1.8971 -0.50159
1.871 -0.54253
1.8429 -0.58038
1.813 -0.61576
1.7814 -0.6492
1.7481 -0.68117
1.7133 -0.71211
1.6769 -0.74237
1.639 -0.77229
1.5997 -0.80218
1.5588 -0.8323
1.5164 -0.86293
1.4725 -0.89431
1.427 -0.92668
1.3798 -0.96026
1.3309 -0.9953
1.2803 -1.032
1.2277 -1.0706
1.1732 -1.1114
1.1165 -1.1546
1.0577 -1.2004
0.99643 -1.249
0.9327 -1.3008
0.8663 -1.3559
0.79705 -1.4146
0.72478 -1.4769
0.64929 -1.5432
0.5704 -1.6133
0.4879 -1.6872
0.40162 -1.7648
0.31137 -1.8456
0.21701 -1.929
0.11844 -2.014
0.015605 -2.0992
-0.091456 -2.1828
-0.20261 -2.2623
-0.31758 -2.335
-0.43594 -2.3973
-0.55707 -2.4454
-0.68017 -2.4751
-0.80422 -2.4825
-0.92799 -2.4637
-1.0501 -2.4163
-1.1691 -2.3386
-1.2835 -2.2311
-1.3917 -2.0957
-1.4926 -1.9363
-1.585 -1.7581
-1.6682 -1.5672
-1.7416 -1.3699
-1.8052 -1.1721
-1.8589 -0.97914
-1.9032 -0.79506
-1.9386 -0.62282
-1.9658 -0.46419
-1.9853 -0.32
-1.998 -0.19025
-2.0046 -0.074391
-2.0057 0.028536
-2.0019 0.1197
-1.9939 0.20037
-1.982 0.27182
-1.9668 0.3353
-1.9486 0.39194
-1.9277 0.44279
-1.9044 0.4888
-1.8789 0.53078
-1.8514 0.56948
-1.822 0.60552
-1.7909 0.63948
-1.7581 0.67185
-1.7237 0.70305
-1.6878 0.73347
-1.6504 0.76346
-1.6115 0.79333
-1.571 0.82336
-1.5291 0.85381
-1.4857 0.88494
-1.4406 0.91699
-1.3939 0.95019
-1.3456 0.98478
-1.2954 1.021
-1.2434 1.059
-1.1895 1.0991
-1.1335 1.1416
-1.0753 1.1865
-1.0148 1.2343
-0.95182 1.2852
-0.88622 1.3393
-0.81783 1.3968
-0.74647 1.4581
-0.67196 1.5232
-0.59409 1.5921
-0.51268 1.665
-0.42753 1.7415
-0.33847 1.8214
-0.24534 1.9042
-0.14803 1.9888
-0.046453 2.0741
0.059367 2.1584
0.16933 2.2394
0.28321 2.3144
0.40062 2.3802
0.52101 2.4329
0.64363 2.4685
0.76751 2.4828
0.8915 2.4722
1.0143 2.4334
1.1343 2.3647
1.2502 2.2659
1.3604 2.1384
1.4636 1.9857
1.5587 1.8124
1.6446 1.6246
1.721 1.4285
1.7874 1.2303
1.844 1.0354
1.8911 0.84837
1.9291 0.67239
1.9586 0.50961
1.9803 0.36112
1.9949 0.22714
2.0032 0.10725
2.0059 0.00061552
2.0035 -0.093896
1.9967 -0.17753
1.9859 -0.25158
1.9716 -0.31729
1.9543 -0.37584
1.9342 -0.4283
1.9116 -0.47565
1.8867 -0.51874
1.8597 -0.55834
1.8309 -0.59511
1.8003 -0.62963
1.768 -0.66242
1.734 -0.69392
1.6986 -0.72454
1.6616 -0.75462
1.6231 -0.78449
1.5832 -0.81444
1.5417 -0.84475
1.4987 -0.87565
1.4541 -0.90741
1.4079 -0.94024
1.36 -0.97439
1.3104 -1.0101
1.259 -1.0476
1.2057 -1.087
1.1503 -1.1288
1.0927 -1.173
1.0329 -1.2199
0.9707 -1.2698
0.9059 -1.3229
0.83835 -1.3794
0.76789 -1.4396
0.69433 -1.5035
0.61748 -1.5713
0.53713 -1.643
0.45311 -1.7185
0.36522 -1.7975
0.27331 -1.8794
0.17724 -1.9636
0.076929 -2.0489
-0.027641 -2.1337
-0.1364 -2.2159
-0.24915 -2.293
-0.36557 -2.3619
-0.48515 -2.4189
-0.6072 -2.46
-0.73082 -2.481
-0.8549 -2.4781
-0.97817 -2.4479
-1.0992 -2.3882
-1.2165 -2.2982
-1.3285 -2.1789
-1.4339 -2.0332
-1.5315 -1.8655
-1.6202 -1.6813
-1.6994 -1.487
-1.7688 -1.2888
-1.8283 -1.0924
-1.8782 -0.90265
-1.9188 -0.72312
-1.9507 -0.55628
-1.9746 -0.40351
-1.9913 -0.26525
-2.0014 -0.14127
-2.0056 -0.030828
-2.0047 0.067142
-1.9991 0.15386
-1.9895 0.23061
-1.9762 0.29866
-1.9597 0.35921
-1.9404 0.41336
-1.9185 0.46213
-1.8943 0.5064
-1.8679 0.54695
-1.8396 0.58449
-1.8095 0.61962
-1.7777 0.65288
-1.7442 0.68472
-1.7092 0.71556
-1.6727 0.74576
-1.6347 0.77566
-1.5951 0.80556
-1.5541 0.83574
-1.5115 0.86644
-1.4674 0.89792
-1.4217 0.93041
-1.3744 0.96415
-1.3253 0.99936
-1.2744 1.0363
-1.2216 1.0751
-1.1669 1.1162
-1.11 1.1596
-1.0509 1.2057

Not sure if you need to add the region inside the limit cycle. However, you can easily add an ellipse as follows:

\draw[fill=yellow,rotate around={25:(axis cs:0,0)}] (axis cs:0,0) ellipse (1.6 and 1.4);

Answer 2

Based on your data (+ added column headers), here is what comes using a pgfplots quiverplot

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usepackage{pgfplotstable}
\pgfplotstableread{
   x               y               u              v 
   5.0000000e+00   5.0000000e+00   1.5375045e-02  -3.8620859e-01
   5.0153750e+00   4.6137914e+00   3.4876123e-02  -8.9247723e-01
   5.0697522e+00   3.2150455e+00   4.7120884e-02  -1.2339311e+00
   5.1096168e+00   2.1459291e+00   3.2612691e-02  -8.9119732e-01
   5.1349776e+00   1.4326509e+00   2.0692523e-02  -5.9536377e-01
   5.1510019e+00   9.5520159e-01   1.3088303e-02  -4.0194104e-01
   5.1611542e+00   6.2876881e-01   8.2438303e-03  -2.7656489e-01
   5.1674895e+00   4.0207181e-01   5.0626974e-03  -1.9276422e-01
   5.1712796e+00   2.4324037e-01   2.9348841e-03  -1.3523094e-01
   5.1733593e+00   1.3160992e-01   1.5130955e-03  -9.4896595e-02
   5.1743058e+00   5.3447176e-02   5.8677480e-04  -6.1018779e-02
   5.1745328e+00   9.5723602e-03   8.0115214e-05  -4.0088716e-02
   5.1744660e+00  -2.6730257e-02  -1.5404170e-04  -3.0781832e-02
   5.1742248e+00  -5.1991305e-02  -3.8495104e-04  -2.6463713e-02
   5.1736961e+00  -7.9657682e-02  -7.2776314e-04  -2.7461272e-02
   5.1727692e+00  -1.0691385e-01  -1.1781516e-03  -2.6064072e-02
   5.1713398e+00  -1.3178583e-01  -1.7339165e-03  -2.3080854e-02
   5.1693014e+00  -1.5307556e-01  -2.4070299e-03  -1.9218339e-02
   5.1665258e+00  -1.7022250e-01  -3.2386956e-03  -1.5049417e-02
   5.1628240e+00  -1.8317439e-01  -4.3388471e-03  -1.1024378e-02
   5.1578481e+00  -1.9227126e-01  -6.0468154e-03  -7.5010259e-03
   5.1507304e+00  -1.9817644e-01  -8.1222890e-03  -4.3633595e-03
   5.1416035e+00  -2.0099798e-01  -9.1715588e-03  -1.9070612e-03
   5.1323873e+00  -2.0199056e-01  -1.3417789e-02  -1.0268839e-03
   5.1147679e+00  -2.0305175e-01  -1.7661691e-02  -8.2170241e-04
   5.0970639e+00  -2.0363397e-01  -2.2391117e-02  -9.9109217e-04
   5.0699857e+00  -2.0503393e-01  -2.3287887e-02  -9.7531501e-04
   5.0504881e+00  -2.0558460e-01  -1.9527635e-02  -8.1399390e-04
   5.0309304e+00  -2.0666192e-01  -2.3042819e-02  -9.7717744e-04
   5.0044025e+00  -2.0753895e-01  -2.3418200e-02  -1.0761901e-03
   4.9840940e+00  -2.0881430e-01  -2.0366409e-02  -9.6606661e-04
   4.9636696e+00  -2.0947109e-01  -2.3082076e-02  -1.0687046e-03
   4.9379299e+00  -2.1095171e-01  -2.6011741e-02  -1.0815549e-03
   4.9116462e+00  -2.1163420e-01  -2.4149461e-02  -1.1651869e-03
   4.8896310e+00  -2.1328208e-01  -2.1354325e-02  -1.0932455e-03
   4.8689375e+00  -2.1382069e-01  -2.2031356e-02  -9.8070964e-04
   4.8455682e+00  -2.1524350e-01  -2.5224340e-02  -1.1723750e-03
   4.8184888e+00  -2.1616544e-01  -2.6552952e-02  -1.3619678e-03
   4.7924623e+00  -2.1796744e-01  -2.4875557e-02  -1.2204887e-03
   4.7687377e+00  -2.1860641e-01  -2.3647924e-02  -1.1125943e-03
   4.7451665e+00  -2.2019263e-01  -2.4990119e-02  -1.2789247e-03
   4.7187575e+00  -2.2116426e-01  -2.7204798e-02  -1.4193725e-03
   4.6907569e+00  -2.2303137e-01  -2.7720404e-02  -1.3878697e-03
   4.6633167e+00  -2.2394000e-01  -2.6718927e-02  -1.3822717e-03
   4.6373190e+00  -2.2579592e-01  -2.6499987e-02  -1.4375387e-03
   4.6103167e+00  -2.2681508e-01  -2.7907499e-02  -1.4895473e-03
   4.5815040e+00  -2.2877501e-01  -2.9544655e-02  -1.5751089e-03
   4.5512274e+00  -2.2996530e-01  -2.9815198e-02  -1.6623333e-03
   4.5218736e+00  -2.3209968e-01  -2.9370497e-02  -1.6568117e-03
   4.4924864e+00  -2.3327892e-01  -2.9796693e-02  -1.6701997e-03
   4.4622803e+00  -2.3544008e-01  -3.1298785e-02  -1.7978494e-03
   4.4298888e+00  -2.3687462e-01  -3.2502356e-02  -1.9229918e-03
   4.3972755e+00  -2.3928606e-01  -3.2808898e-02  -1.9458717e-03
   4.3642710e+00  -2.4076636e-01  -3.2973966e-02  -1.9846557e-03
   4.3313276e+00  -2.4325537e-01  -3.3929627e-02  -2.0981889e-03
   4.2964118e+00  -2.4496274e-01  -3.5330052e-02  -2.2230522e-03
   4.2606675e+00  -2.4770148e-01  -3.6500550e-02  -2.3201369e-03
   4.2234107e+00  -2.4960302e-01  -3.7109322e-02  -2.4210438e-03
   4.1864489e+00  -2.5254356e-01  -3.7866850e-02  -2.5258135e-03
   4.1476770e+00  -2.5465464e-01  -3.9130255e-02  -2.6549304e-03
   4.1081884e+00  -2.5785342e-01  -4.0829064e-02  -2.8266337e-03
   4.0660188e+00  -2.6030791e-01  -4.2127466e-02  -3.0008646e-03
   4.0239334e+00  -2.6385515e-01  -4.3290003e-02  -3.1505155e-03
   3.9794388e+00  -2.6660894e-01  -4.4613726e-02  -3.3248984e-03
   3.9347060e+00  -2.7050495e-01  -4.6660425e-02  -3.5725176e-03
   3.8861180e+00  -2.7375398e-01  -4.8596167e-02  -3.8338285e-03
   3.8375136e+00  -2.7817261e-01  -5.0694549e-02  -4.1079148e-03
   3.7847289e+00  -2.8196981e-01  -5.2563008e-02  -4.3978063e-03
   3.7323876e+00  -2.8696822e-01  -5.5288920e-02  -4.7822653e-03
   3.6741511e+00  -2.9153434e-01  -5.7922409e-02  -5.1901599e-03
   3.6165428e+00  -2.9734854e-01  -6.1603931e-02  -5.7265594e-03
   3.5509432e+00  -3.0298746e-01  -6.4589583e-02  -6.2588600e-03
   3.4873636e+00  -3.0986626e-01  -6.9210468e-02  -7.0094933e-03
   3.4125223e+00  -3.1700644e-01  -7.3036226e-02  -7.7519262e-03
   3.3412912e+00  -3.2537011e-01  -8.0258291e-02  -8.9849554e-03
   3.2520057e+00  -3.3497635e-01  -8.5032194e-02  -1.0080538e-02
   3.1712268e+00  -3.4553119e-01  -9.5834397e-02  -1.2154307e-02
   3.0603369e+00  -3.5928497e-01  -1.0165388e-01  -1.3825426e-02
   2.9679190e+00  -3.7318204e-01  -9.5628158e-02  -1.4342106e-02
   2.8690806e+00  -3.8796918e-01  -1.0089907e-01  -1.5993383e-02
   2.7661209e+00  -4.0516881e-01  -1.3008578e-01  -2.2923141e-02
   2.6089090e+00  -4.3381546e-01  -1.4845392e-01  -2.9258572e-02
   2.4692130e+00  -4.6368595e-01  -1.5682481e-01  -3.5970836e-02
   2.2952594e+00  -5.0575713e-01  -1.7213529e-01  -4.5530553e-02
   2.1249425e+00  -5.5474706e-01  -1.8138057e-01  -5.7431808e-02
   1.9324982e+00  -6.2062075e-01  -2.0120486e-01  -7.6809066e-02
   1.7225327e+00  -7.0836519e-01  -2.1977012e-01  -1.0325325e-01
   1.4929580e+00  -8.2712725e-01  -2.3855726e-01  -1.3888518e-01
   1.2454182e+00  -9.8613554e-01  -2.5728390e-01  -1.8454544e-01
   9.7839018e-01  -1.1962181e+00  -2.8342242e-01  -2.4506191e-01
   6.7857338e-01  -1.4762594e+00  -3.3512752e-01  -3.3396931e-01
   3.0813515e-01  -1.8641568e+00  -3.7553782e-01  -3.9091655e-01
  -7.2502262e-02  -2.2580925e+00  -3.2727074e-01  -3.1513960e-01
  -3.4640633e-01  -2.4944360e+00  -2.8582962e-01  -2.0094573e-01
  -6.4416150e-01  -2.6599839e+00  -2.9335209e-01  -9.3774236e-02
  -9.3311051e-01  -2.6819844e+00  -2.9488789e-01   7.9303745e-02
  -1.2339373e+00  -2.5013764e+00  -2.9067267e-01   3.0030151e-01
  -1.5144558e+00  -2.0813814e+00  -2.3212972e-01   4.3514870e-01
  -1.6981967e+00  -1.6310790e+00  -1.5268708e-01   4.2769331e-01
  -1.8198300e+00  -1.2259948e+00  -1.0477615e-01   3.9064105e-01
  -1.9077490e+00  -8.4979692e-01  -7.5220260e-02   3.6535882e-01
  -1.9702705e+00  -4.9527714e-01  -5.0581638e-02   3.6205433e-01
  -2.0089123e+00  -1.2568827e-01  -2.1062521e-02   2.5210788e-01
  -2.0123956e+00   8.9386143e-03   3.0282864e-04   1.2309766e-01
  -2.0083067e+00   1.2050706e-01   6.8649971e-03   9.9618557e-02
  -1.9986656e+00   2.0817573e-01   1.3888147e-02   8.8106964e-02
  -1.9805304e+00   2.9672099e-01   2.3493137e-02   8.6338440e-02
  -1.9516793e+00   3.8085261e-01   3.5410665e-02   8.1071630e-02
  -1.9097090e+00   4.5886425e-01   5.0163597e-02   7.5567335e-02
  -1.8513521e+00   5.3198728e-01   6.8987037e-02   7.2592965e-02
  -1.7717350e+00   6.0405018e-01   9.3861320e-02   7.5023456e-02
  -1.6636295e+00   6.8203419e-01   1.2695354e-01   8.6590129e-02
  -1.5178279e+00   7.7723043e-01   1.6794491e-01   1.1147654e-01
  -1.3277396e+00   9.0498727e-01   2.1102387e-01   1.5165932e-01
  -1.0957801e+00   1.0805491e+00   2.5111312e-01   2.0673793e-01
  -8.2551340e-01   1.3184631e+00   2.9784340e-01   2.8265936e-01
  -5.0009333e-01   1.6458678e+00   3.4815941e-01   3.6122922e-01
  -1.2919459e-01   2.0409216e+00   3.2602662e-01   3.3665136e-01
   1.5195992e-01   2.3191705e+00   2.9838308e-01   2.6066088e-01
   4.6757156e-01   2.5622433e+00   3.0601859e-01   1.7770385e-01
   7.6399710e-01   2.6745782e+00   2.9247767e-01   3.0969255e-02
   1.0525269e+00   2.6241818e+00   2.9128230e-01  -1.6186784e-01
   1.3465617e+00   2.3508425e+00   2.4601433e-01  -3.1068418e-01
   1.5445556e+00   2.0028135e+00   1.8044909e-01  -3.8204061e-01
   1.7074599e+00   1.5867613e+00   1.4017150e-01  -4.0752963e-01
   1.8248986e+00   1.1877542e+00   1.0140544e-01  -3.8573509e-01
   1.9102708e+00   8.1529110e-01   7.2859882e-02  -3.6218176e-01
   1.9706183e+00   4.6339070e-01   4.8189777e-02  -3.6427720e-01
   2.0066503e+00   8.6736710e-02   1.8659083e-02  -2.5250145e-01
   2.0079365e+00  -4.1612193e-02  -2.3401563e-03  -1.1731702e-01
   2.0019700e+00  -1.4789733e-01  -9.0772045e-03  -9.7747464e-02
   1.9897821e+00  -2.3710712e-01  -1.6821048e-02  -8.8513394e-02
   1.9683279e+00  -3.2492411e-01  -2.7205202e-02  -8.5150927e-02
   1.9353717e+00  -4.0740897e-01  -4.0019478e-02  -7.9494340e-02
   1.8882889e+00  -4.8391279e-01  -5.6006188e-02  -7.4560642e-02
   1.8233593e+00  -5.5653026e-01  -7.6650078e-02  -7.3072124e-02
   1.7349888e+00  -6.3005704e-01  -1.0411806e-01  -7.8144155e-02
   1.6151232e+00  -7.1281857e-01  -1.4016767e-01  -9.3828091e-02
   1.4546534e+00  -8.1771323e-01  -1.8273477e-01  -1.2392570e-01
   1.2496536e+00  -9.6066996e-01  -2.2499040e-01  -1.6927601e-01
   1.0046726e+00  -1.1562652e+00  -2.6534157e-01  -2.3022966e-01
   7.1897052e-01  -1.4211293e+00  -3.2260991e-01  -3.1949462e-01
   3.5945282e-01  -1.7952545e+00  -3.6834533e-01  -3.8483364e-01
  -1.7720148e-02  -2.1907966e+00  -3.2545170e-01  -3.2153939e-01
  -2.9145058e-01  -2.4383333e+00  -2.8694493e-01  -2.1743893e-01
  -5.9161002e-01  -2.6256744e+00  -2.9488168e-01  -1.1876703e-01
  -8.8121394e-01  -2.6758673e+00  -2.9212345e-01   4.2654315e-02
  -1.1758569e+00  -2.5403658e+00  -2.8958294e-01   2.5354649e-01
  -1.4603798e+00  -2.1687743e+00  -2.4488695e-01   4.1728897e-01
  -1.6656308e+00  -1.7057879e+00  -1.4133867e-01   3.4676055e-01
  -1.7430571e+00  -1.4752532e+00  -7.7426317e-02   2.3053465e-01
}\loadedtable

\begin{document}
\begin{tikzpicture}    
    \begin{axis}
        \addplot[-stealth,red,quiver={u=\thisrow{u},v=\thisrow{v}}] table {\loadedtable};
    \end{axis}
\end{tikzpicture}
\end{document}

And here is another solution without column headers based on the column index, using an external file as the data source

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{filecontents*}{mydata.tsv}
   5.0000000e+00   5.0000000e+00   1.5375045e-02  -3.8620859e-01
   5.0153750e+00   4.6137914e+00   3.4876123e-02  -8.9247723e-01
   5.0697522e+00   3.2150455e+00   4.7120884e-02  -1.2339311e+00
   5.1096168e+00   2.1459291e+00   3.2612691e-02  -8.9119732e-01
   5.1349776e+00   1.4326509e+00   2.0692523e-02  -5.9536377e-01
   5.1510019e+00   9.5520159e-01   1.3088303e-02  -4.0194104e-01
   5.1611542e+00   6.2876881e-01   8.2438303e-03  -2.7656489e-01
   5.1674895e+00   4.0207181e-01   5.0626974e-03  -1.9276422e-01
   5.1712796e+00   2.4324037e-01   2.9348841e-03  -1.3523094e-01
   5.1733593e+00   1.3160992e-01   1.5130955e-03  -9.4896595e-02
   5.1743058e+00   5.3447176e-02   5.8677480e-04  -6.1018779e-02
   5.1745328e+00   9.5723602e-03   8.0115214e-05  -4.0088716e-02
   5.1744660e+00  -2.6730257e-02  -1.5404170e-04  -3.0781832e-02
   5.1742248e+00  -5.1991305e-02  -3.8495104e-04  -2.6463713e-02
   5.1736961e+00  -7.9657682e-02  -7.2776314e-04  -2.7461272e-02
   5.1727692e+00  -1.0691385e-01  -1.1781516e-03  -2.6064072e-02
   5.1713398e+00  -1.3178583e-01  -1.7339165e-03  -2.3080854e-02
   5.1693014e+00  -1.5307556e-01  -2.4070299e-03  -1.9218339e-02
   5.1665258e+00  -1.7022250e-01  -3.2386956e-03  -1.5049417e-02
   5.1628240e+00  -1.8317439e-01  -4.3388471e-03  -1.1024378e-02
   5.1578481e+00  -1.9227126e-01  -6.0468154e-03  -7.5010259e-03
   5.1507304e+00  -1.9817644e-01  -8.1222890e-03  -4.3633595e-03
   5.1416035e+00  -2.0099798e-01  -9.1715588e-03  -1.9070612e-03
   5.1323873e+00  -2.0199056e-01  -1.3417789e-02  -1.0268839e-03
   5.1147679e+00  -2.0305175e-01  -1.7661691e-02  -8.2170241e-04
   5.0970639e+00  -2.0363397e-01  -2.2391117e-02  -9.9109217e-04
   5.0699857e+00  -2.0503393e-01  -2.3287887e-02  -9.7531501e-04
   5.0504881e+00  -2.0558460e-01  -1.9527635e-02  -8.1399390e-04
   5.0309304e+00  -2.0666192e-01  -2.3042819e-02  -9.7717744e-04
   5.0044025e+00  -2.0753895e-01  -2.3418200e-02  -1.0761901e-03
   4.9840940e+00  -2.0881430e-01  -2.0366409e-02  -9.6606661e-04
   4.9636696e+00  -2.0947109e-01  -2.3082076e-02  -1.0687046e-03
   4.9379299e+00  -2.1095171e-01  -2.6011741e-02  -1.0815549e-03
   4.9116462e+00  -2.1163420e-01  -2.4149461e-02  -1.1651869e-03
   4.8896310e+00  -2.1328208e-01  -2.1354325e-02  -1.0932455e-03
   4.8689375e+00  -2.1382069e-01  -2.2031356e-02  -9.8070964e-04
   4.8455682e+00  -2.1524350e-01  -2.5224340e-02  -1.1723750e-03
   4.8184888e+00  -2.1616544e-01  -2.6552952e-02  -1.3619678e-03
   4.7924623e+00  -2.1796744e-01  -2.4875557e-02  -1.2204887e-03
   4.7687377e+00  -2.1860641e-01  -2.3647924e-02  -1.1125943e-03
   4.7451665e+00  -2.2019263e-01  -2.4990119e-02  -1.2789247e-03
   4.7187575e+00  -2.2116426e-01  -2.7204798e-02  -1.4193725e-03
   4.6907569e+00  -2.2303137e-01  -2.7720404e-02  -1.3878697e-03
   4.6633167e+00  -2.2394000e-01  -2.6718927e-02  -1.3822717e-03
   4.6373190e+00  -2.2579592e-01  -2.6499987e-02  -1.4375387e-03
   4.6103167e+00  -2.2681508e-01  -2.7907499e-02  -1.4895473e-03
   4.5815040e+00  -2.2877501e-01  -2.9544655e-02  -1.5751089e-03
   4.5512274e+00  -2.2996530e-01  -2.9815198e-02  -1.6623333e-03
   4.5218736e+00  -2.3209968e-01  -2.9370497e-02  -1.6568117e-03
   4.4924864e+00  -2.3327892e-01  -2.9796693e-02  -1.6701997e-03
   4.4622803e+00  -2.3544008e-01  -3.1298785e-02  -1.7978494e-03
   4.4298888e+00  -2.3687462e-01  -3.2502356e-02  -1.9229918e-03
   4.3972755e+00  -2.3928606e-01  -3.2808898e-02  -1.9458717e-03
   4.3642710e+00  -2.4076636e-01  -3.2973966e-02  -1.9846557e-03
   4.3313276e+00  -2.4325537e-01  -3.3929627e-02  -2.0981889e-03
   4.2964118e+00  -2.4496274e-01  -3.5330052e-02  -2.2230522e-03
   4.2606675e+00  -2.4770148e-01  -3.6500550e-02  -2.3201369e-03
   4.2234107e+00  -2.4960302e-01  -3.7109322e-02  -2.4210438e-03
   4.1864489e+00  -2.5254356e-01  -3.7866850e-02  -2.5258135e-03
   4.1476770e+00  -2.5465464e-01  -3.9130255e-02  -2.6549304e-03
   4.1081884e+00  -2.5785342e-01  -4.0829064e-02  -2.8266337e-03
   4.0660188e+00  -2.6030791e-01  -4.2127466e-02  -3.0008646e-03
   4.0239334e+00  -2.6385515e-01  -4.3290003e-02  -3.1505155e-03
   3.9794388e+00  -2.6660894e-01  -4.4613726e-02  -3.3248984e-03
   3.9347060e+00  -2.7050495e-01  -4.6660425e-02  -3.5725176e-03
   3.8861180e+00  -2.7375398e-01  -4.8596167e-02  -3.8338285e-03
   3.8375136e+00  -2.7817261e-01  -5.0694549e-02  -4.1079148e-03
   3.7847289e+00  -2.8196981e-01  -5.2563008e-02  -4.3978063e-03
   3.7323876e+00  -2.8696822e-01  -5.5288920e-02  -4.7822653e-03
   3.6741511e+00  -2.9153434e-01  -5.7922409e-02  -5.1901599e-03
   3.6165428e+00  -2.9734854e-01  -6.1603931e-02  -5.7265594e-03
   3.5509432e+00  -3.0298746e-01  -6.4589583e-02  -6.2588600e-03
   3.4873636e+00  -3.0986626e-01  -6.9210468e-02  -7.0094933e-03
   3.4125223e+00  -3.1700644e-01  -7.3036226e-02  -7.7519262e-03
   3.3412912e+00  -3.2537011e-01  -8.0258291e-02  -8.9849554e-03
   3.2520057e+00  -3.3497635e-01  -8.5032194e-02  -1.0080538e-02
   3.1712268e+00  -3.4553119e-01  -9.5834397e-02  -1.2154307e-02
   3.0603369e+00  -3.5928497e-01  -1.0165388e-01  -1.3825426e-02
   2.9679190e+00  -3.7318204e-01  -9.5628158e-02  -1.4342106e-02
   2.8690806e+00  -3.8796918e-01  -1.0089907e-01  -1.5993383e-02
   2.7661209e+00  -4.0516881e-01  -1.3008578e-01  -2.2923141e-02
   2.6089090e+00  -4.3381546e-01  -1.4845392e-01  -2.9258572e-02
   2.4692130e+00  -4.6368595e-01  -1.5682481e-01  -3.5970836e-02
   2.2952594e+00  -5.0575713e-01  -1.7213529e-01  -4.5530553e-02
   2.1249425e+00  -5.5474706e-01  -1.8138057e-01  -5.7431808e-02
   1.9324982e+00  -6.2062075e-01  -2.0120486e-01  -7.6809066e-02
   1.7225327e+00  -7.0836519e-01  -2.1977012e-01  -1.0325325e-01
   1.4929580e+00  -8.2712725e-01  -2.3855726e-01  -1.3888518e-01
   1.2454182e+00  -9.8613554e-01  -2.5728390e-01  -1.8454544e-01
   9.7839018e-01  -1.1962181e+00  -2.8342242e-01  -2.4506191e-01
   6.7857338e-01  -1.4762594e+00  -3.3512752e-01  -3.3396931e-01
   3.0813515e-01  -1.8641568e+00  -3.7553782e-01  -3.9091655e-01
  -7.2502262e-02  -2.2580925e+00  -3.2727074e-01  -3.1513960e-01
  -3.4640633e-01  -2.4944360e+00  -2.8582962e-01  -2.0094573e-01
  -6.4416150e-01  -2.6599839e+00  -2.9335209e-01  -9.3774236e-02
  -9.3311051e-01  -2.6819844e+00  -2.9488789e-01   7.9303745e-02
  -1.2339373e+00  -2.5013764e+00  -2.9067267e-01   3.0030151e-01
  -1.5144558e+00  -2.0813814e+00  -2.3212972e-01   4.3514870e-01
  -1.6981967e+00  -1.6310790e+00  -1.5268708e-01   4.2769331e-01
  -1.8198300e+00  -1.2259948e+00  -1.0477615e-01   3.9064105e-01
  -1.9077490e+00  -8.4979692e-01  -7.5220260e-02   3.6535882e-01
  -1.9702705e+00  -4.9527714e-01  -5.0581638e-02   3.6205433e-01
  -2.0089123e+00  -1.2568827e-01  -2.1062521e-02   2.5210788e-01
  -2.0123956e+00   8.9386143e-03   3.0282864e-04   1.2309766e-01
  -2.0083067e+00   1.2050706e-01   6.8649971e-03   9.9618557e-02
  -1.9986656e+00   2.0817573e-01   1.3888147e-02   8.8106964e-02
  -1.9805304e+00   2.9672099e-01   2.3493137e-02   8.6338440e-02
  -1.9516793e+00   3.8085261e-01   3.5410665e-02   8.1071630e-02
  -1.9097090e+00   4.5886425e-01   5.0163597e-02   7.5567335e-02
  -1.8513521e+00   5.3198728e-01   6.8987037e-02   7.2592965e-02
  -1.7717350e+00   6.0405018e-01   9.3861320e-02   7.5023456e-02
  -1.6636295e+00   6.8203419e-01   1.2695354e-01   8.6590129e-02
  -1.5178279e+00   7.7723043e-01   1.6794491e-01   1.1147654e-01
  -1.3277396e+00   9.0498727e-01   2.1102387e-01   1.5165932e-01
  -1.0957801e+00   1.0805491e+00   2.5111312e-01   2.0673793e-01
  -8.2551340e-01   1.3184631e+00   2.9784340e-01   2.8265936e-01
  -5.0009333e-01   1.6458678e+00   3.4815941e-01   3.6122922e-01
  -1.2919459e-01   2.0409216e+00   3.2602662e-01   3.3665136e-01
   1.5195992e-01   2.3191705e+00   2.9838308e-01   2.6066088e-01
   4.6757156e-01   2.5622433e+00   3.0601859e-01   1.7770385e-01
   7.6399710e-01   2.6745782e+00   2.9247767e-01   3.0969255e-02
   1.0525269e+00   2.6241818e+00   2.9128230e-01  -1.6186784e-01
   1.3465617e+00   2.3508425e+00   2.4601433e-01  -3.1068418e-01
   1.5445556e+00   2.0028135e+00   1.8044909e-01  -3.8204061e-01
   1.7074599e+00   1.5867613e+00   1.4017150e-01  -4.0752963e-01
   1.8248986e+00   1.1877542e+00   1.0140544e-01  -3.8573509e-01
   1.9102708e+00   8.1529110e-01   7.2859882e-02  -3.6218176e-01
   1.9706183e+00   4.6339070e-01   4.8189777e-02  -3.6427720e-01
   2.0066503e+00   8.6736710e-02   1.8659083e-02  -2.5250145e-01
   2.0079365e+00  -4.1612193e-02  -2.3401563e-03  -1.1731702e-01
   2.0019700e+00  -1.4789733e-01  -9.0772045e-03  -9.7747464e-02
   1.9897821e+00  -2.3710712e-01  -1.6821048e-02  -8.8513394e-02
   1.9683279e+00  -3.2492411e-01  -2.7205202e-02  -8.5150927e-02
   1.9353717e+00  -4.0740897e-01  -4.0019478e-02  -7.9494340e-02
   1.8882889e+00  -4.8391279e-01  -5.6006188e-02  -7.4560642e-02
   1.8233593e+00  -5.5653026e-01  -7.6650078e-02  -7.3072124e-02
   1.7349888e+00  -6.3005704e-01  -1.0411806e-01  -7.8144155e-02
   1.6151232e+00  -7.1281857e-01  -1.4016767e-01  -9.3828091e-02
   1.4546534e+00  -8.1771323e-01  -1.8273477e-01  -1.2392570e-01
   1.2496536e+00  -9.6066996e-01  -2.2499040e-01  -1.6927601e-01
   1.0046726e+00  -1.1562652e+00  -2.6534157e-01  -2.3022966e-01
   7.1897052e-01  -1.4211293e+00  -3.2260991e-01  -3.1949462e-01
   3.5945282e-01  -1.7952545e+00  -3.6834533e-01  -3.8483364e-01
  -1.7720148e-02  -2.1907966e+00  -3.2545170e-01  -3.2153939e-01
  -2.9145058e-01  -2.4383333e+00  -2.8694493e-01  -2.1743893e-01
  -5.9161002e-01  -2.6256744e+00  -2.9488168e-01  -1.1876703e-01
  -8.8121394e-01  -2.6758673e+00  -2.9212345e-01   4.2654315e-02
  -1.1758569e+00  -2.5403658e+00  -2.8958294e-01   2.5354649e-01
  -1.4603798e+00  -2.1687743e+00  -2.4488695e-01   4.1728897e-01
  -1.6656308e+00  -1.7057879e+00  -1.4133867e-01   3.4676055e-01
  -1.7430571e+00  -1.4752532e+00  -7.7426317e-02   2.3053465e-01
\end{filecontents*}

\begin{document}
\begin{tikzpicture}    
    \begin{axis}
        \addplot[-stealth,red,quiver={u=\thisrowno{2},v=\thisrowno{3}}] table[x expr=\thisrowno{0},y expr=\thisrowno{1}] {mydata.tsv};
    \end{axis}
\end{tikzpicture}
\end{document}

EDIT Here is a last proposal based on decorations as noted by @Schrödinger's cat.

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usetikzlibrary{decorations.markings,arrows.meta}
\tikzset{arrow decoration/.style={
 postaction={
  decorate,
  decoration={
   markings,
   mark=between positions 4.5mm and 1 step 5mm with {\arrow[]{stealth};}
  }
 },
 red,
 dash pattern=on 4mm off 1mm on 4mm off 1mm
}}

\begin{document}
\begin{tikzpicture}    
    \begin{axis}
        \addplot[red,arrow decoration,smooth] table[x expr=\thisrowno{0},y expr=\thisrowno{1}] {mydata.tsv};
    \end{axis}
\end{tikzpicture}
\end{document}