乳胶中的相平面图

Question

有没有方法可以直接在乳胶中构建相平面图？我想根据矩阵的特征值绘制这样的图。

例如，如果一个 2×2 矩阵的两个特征值都是实数、不同且为负数，则应该得到该图（我在 MATLAB 中绘制）。

Answer 1

我认为这个问题有两个方面：

1. 如何在路径上添加弯曲箭头？
2. 如何猜测您所展示的曲线（RG 流？）的参数化。

至于 1.，我正在使用这些风格，至于 2.，我很快就猜到了一些看起来很相似的东西。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{arrows.meta,bending,decorations.markings} 
% from https://tex.stackexchange.com/a/430239/121799
\tikzset{% inspired by https://tex.stackexchange.com/a/316050/121799
    arc arrow/.style args={%
    to pos #1 with length #2 and options #3}{
    decoration={
        markings,
         mark=at position 0 with {\pgfextra{%
         \pgfmathsetmacro{\tmpArrowTime}{#2/(\pgfdecoratedpathlength)}
         \xdef\tmpArrowTime{\tmpArrowTime}}},
        mark=at position {#1-\tmpArrowTime} with {\coordinate(@1);},
        mark=at position {#1-2*\tmpArrowTime/3} with {\coordinate(@2);},
        mark=at position {#1-\tmpArrowTime/3} with {\coordinate(@3);},
        mark=at position {#1} with {\coordinate(@4);
        \draw[-{Stealth[length=#2,bend,#3]}]       
        (@1) .. controls (@2) and (@3) .. (@4);},
        },
     postaction=decorate,
     }
}


\begin{document}
\begin{tikzpicture}[thick,
curved arrow/.style={arc arrow={to pos #1 with length 2mm and options {}}},
reversed curved arrow/.style={arc arrow={to pos #1 with length 2mm and options reversed}}]
 \begin{scope}
  \draw (-3,0) -- (3,0) node[below] {$x_1$};
  \draw (0,-3) -- (0,3) node[left] {$x_2$};
  \foreach \X in {2,2.5}
  {\draw[rotate=45,curved arrow=0.25] circle (\X cm and 0.4*\X cm);}
 \end{scope}
 \begin{scope}[xshift=7cm]
  \draw (-3,0) -- (3,0) node[below] {$x_1$};
  \draw (0,-3) -- (0,3) node[left] {$x_2$};
  \draw (-120:pi) -- (60:pi) node[pos=0.9,left]{$v_2$};
  \draw[rotate=-20,reversed curved arrow=0.2,curved arrow=0.8]
  plot[variable=\x,domain=-1.8:1.8,samples=101] (\x,-\x^3+2*\x);
  \draw[rotate=-10,reversed curved arrow=0.2,curved arrow=0.8]
  plot[variable=\x,domain=-1.8:1.8,samples=101] (1.5*\x,-\x^3+2*\x);
 \end{scope}
\end{tikzpicture}
\end{document}