很抱歉我没有提供我的问题的代码，因为我通常总是提供代码，但这次我不太确定如何实现我的目标，这就是为什么我需要你的帮助。所以我正在尝试绘制范德波尔振荡器的相位图。我希望绘图看起来是这样的：
我正在尝试强调吸引力区域。我的问题如下：
1）我不熟悉箭筒，也不知道如何使用它
2）我可以从 Matlab 获取数据，但我不知道如何使用它
当然，如果能给出一个关于如何实现这一点的代码示例就更好了，但给出一些关于如何将 tikz 与 Matlab 结合使用的提示也不错。到目前为止，我使用 pgfplots 中所述的命令导出了一个包含 4 列（x、y、u、v）的数据集，但我真的不确定如何使用它们。有没有办法让 pgf 使用现成的数据？
我感谢所有的帮助
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编辑：我添加了一些从 MATLAB 模拟中积累的数据。
matlab 图如下所示：[ 
]
列为 1：x 2：y 3：u 4：v
答案1
这范德波尔振荡器可以表示为：
\dot{x}=y, \dot{y}=\mu (1-x^2)y-x
在 Matlab 中模拟该系统，从不同的初始条件和\mu=0.8，我们将得到收敛到稳定极限环的轨迹。
要在 LaTeX 中绘制此图，我们可以使用 Pgfplots 包。我们区分两个部分：
- 轨迹和极限环：我们可以从 matlab 导出数据并使用
\addplot[options] file{filename.txt} - 矢量场：基于系统动力学，我们可以
quiver利用\addplot3
相应的代码如下：
\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 包含您从 Matlatb 获得的数据（x 和 y 轨迹）。在这种情况下，它对应于极限环（稳态轨迹）。模拟后，您可以提取稳态数据以仅获取极限环部分而不是瞬态部分。
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-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
不确定是否需要在极限环内添加区域。不过，您可以轻松添加椭圆，如下所示：
\draw[fill=yellow,rotate around={25:(axis cs:0,0)}] (axis cs:0,0) ellipse (1.6 and 1.4);
答案2
根据您的数据（+添加的列标题），以下是使用pgfplots quiver图表得出的结果
\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}
这是另一种基于列索引的解决方案，没有列标题，使用外部文件作为数据源
\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
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\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}
编辑decorations这是根据@Schrödinger's cat 所述的最后一项提议。
\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}
