Cfrgtkky

Is there any method to construct phase plane diagrams directly in latex? I want to sketch plots like these based on eigenvalues of a matrix.

For e.g., if both the eigenvalues of a 2-by-2 matrix are real, distinct, and negative, this plot should result (which I have drawn in MATLAB).

This question has IMHO two aspects:

1. How can one add bent arrows to a path?


2. How can one guess the parametrizations of the curves (RG flows?) you show.

As for 1., I am using these styles, and as for 2., I quickly guessed something that looks similar.

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)}

         xdeftmpArrowTime{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}