Improving the Trace Determinant Diagram

I am using the Trace Determinant Diagram provided in this answer.

Note that each phase portrait is created as follows,

newinlaysaddle{saddle}%
  {begin{tikzpicture}[scale=inlayscale]
     foreach sx in {+,-}
      {draw[flow] (sx4,0) -- (0,0);
       draw[flow] (0,0) -- (0,sx4);
       foreach sy in {+,-}
         foreach a/b/c/d in {2.8/0.3/0.7/0.6,3.9/0.4/1.3/1.1}
           draw[flow] (sxa,syb)
              .. controls (sxc,syd) and (sxd,syc)
              .. (sxb,sya);
      }

The complete code is

% Poincaré Diagram: Classification of Phase Portaits in the (det A,Tr A)-plane
% Author: Gernot Salzer
% Based on a drawing by Douglas R. Hundley, people.whitman.edu/~hundledr/courses/M244/Poincare.pdf
documentclass[border=1mm]{standalone}
usepackage{tikz}
usetikzlibrary{decorations.markings,arrows}

tikzset
  {every pin/.style={pin edge={<-}}
  ,>=stealth
  ,flow/.style=
    {decoration=
      {markings
      ,mark=at position #1 with {arrow{>}}
      }
    ,postaction={decorate}
    }
  ,flow/.default=0.5
  }
newcommandinlayscale{}
newcommandinlaycaption[1]{{sffamilyscriptsize#1}}
newcommandnewinlay[4][0.18]%
  {renewcommandinlayscale{#1}%
   newsavebox#2%
   savebox#2%
     {begin{tabular}{@{}c@{}}
        #4[-1ex]
        inlaycaption{#3}[-1ex]
      end{tabular}%
     }%
  }
newcommandinlay[1]{usebox{#1}}
newcommandTr{mathop{mathrm{Tr}}}

newinlaysaddle{saddle}%
  {begin{tikzpicture}[scale=inlayscale]
     foreach sx in {+,-}
      {draw[flow] (sx4,0) -- (0,0);
       draw[flow] (0,0) -- (0,sx4);
       foreach sy in {+,-}
         foreach a/b/c/d in {2.8/0.3/0.7/0.6,3.9/0.4/1.3/1.1}
           draw[flow] (sxa,syb)
              .. controls (sxc,syd) and (sxd,syc)
              .. (sxb,sya);
      }
   end{tikzpicture}%
  }

newinlaysink{sink}%
  {begin{tikzpicture}[scale=inlayscale]
    foreach sx in {+,-}
     {draw[flow] (sx4,0) -- (0,0);
      draw[flow] (0,sx4) -- (0,0);
      foreach sy in {+,-}
         foreach a/b in {2/1,3/0.44}
          draw[flow,domain=sxa:0] plot (x, {syb*x*x});
     }
   end{tikzpicture}%
  }

newinlaysource{source}%
  {begin{tikzpicture}[scale=inlayscale]
     foreach sx in {+,-}
      {draw[flow] (0,0) -- (sx4,0);
       draw[flow] (0,0) -- (0,sx4);
       foreach sy in {+,-}
         foreach a/b in {2/1,3/0.44}
           draw[flow,domain=0:sxa] plot (x, {syb*x*x});
      }
   end{tikzpicture}%
  }

newinlaystablefp{line of stable fixed points}%
  {begin{tikzpicture}[scale=inlayscale]
    draw (-4,0) -- (4,0);
    foreach s in {+,-}
     {draw[flow] (0,s4) -- (0,0);
      foreach x in {-3,-2,-1,1,2,3}
        draw[flow] (x,s3) -- (x,0);
     }
   end{tikzpicture}%
  }

newinlayunstablefp{line of unstable fixed points}%
  {begin{tikzpicture}[scale=inlayscale]
     draw (-4,0) -- (4,0);
     foreach s in {+,-}
      {draw[flow] (0,0) -- (0,s4);
       foreach x in {-3,-2,-1,1,2,3}
         draw[flow] (x,0) -- (x,s3);
      }
   end{tikzpicture}%
  }

newinlayspiralsink{spiral sink}%
  {begin{tikzpicture}[scale=inlayscale]
     draw (-4,0) -- (4,0);
     draw (0,-4) -- (0,4);
     draw[samples=100,smooth,domain=27:7] plot ({x r}: {0.005*x*x});
     draw[->] ({26 r}: {0.005*26*26}) -- +(0.01,-0.01);
   end{tikzpicture}%
  }

newinlayspiralsource{spiral source}%
  {begin{tikzpicture}[scale=inlayscale]
     draw (-4,0) -- (4,0);
     draw (0,-4) -- (0,4);
     draw [samples=100,smooth,domain=10:28] plot ({-x r}: {0.005*x*x});
     draw[<-] ({-27.5 r}: {0.005*27.5*27.5}) -- +(0.01,-0.008);
   end{tikzpicture}%
  }

newinlay[0.15]centre{center}%
  {begin{tikzpicture}[scale=inlayscale]
     draw (-4,0) -- (4,0);
     draw (0,-4) -- (0,4);
     foreach r in {1,2,3} draw[flow=0.63] (r,0) arc (0:-360:r cm);
   end{tikzpicture}%
  }

newinlaydegensink{degenerate sink}%
  {begin{tikzpicture}[scale=inlayscale]
     draw (0,-4) -- (0,4);
     draw[flow] (-4,0) -- (0,0);
     draw[flow] (4,0) -- (0,0);
     draw[flow] (-3.5,3.5) .. controls (4,1.5) and (4,1).. (0,0);
     draw[flow] (3.5,-3.5) .. controls (-4,-1.5) and (-4,-1) .. (0,0);
     draw[flow] (-3.5,2.5) .. controls (2,1) and (2,0.8).. (0,0);
     draw[flow] (3.5,-2.5) .. controls (-2,-1) and (-2,-0.8) .. (0,0);
   end{tikzpicture}%
  }

newinlaydegensource{degenerate source}%
  {begin{tikzpicture}[scale=inlayscale]
     draw (0,-4) -- (0,4);
     draw[flow] (0,0) -- (-4,0);
     draw[flow] (0,0) -- (4,0);
     draw[flow] (0,0) .. controls (4,1.5) and (4,1).. (-3.5,3.5);
     draw[flow] (0,0) .. controls (-4,-1.5) and (-4,-1) .. (3.5,-3.5);
     draw[flow] (0,0) .. controls (2,1) and (2,0.8).. (-3.5,2.5);
     draw[flow] (0,0) .. controls (-2,-1) and (-2,-0.8) .. (3.5,-2.5);
   end{tikzpicture}%
  }

begin{document}
begin{tikzpicture}[line cap=round,line join=round]
  % Main diagram
  draw[line width=1pt,->] (0,-0.3) -- (0, 4.7) coordinate (+y);
  draw[line width=1pt,->] (-5,0) -- ( 5,0) coordinate (+x);
  draw[line width=1pt, domain=-4:4] plot (x, {0.25*x*x});
  node at (+y) [label={[above,yshift=0.8cm]%
    {sffamilylarge Poincar'e Diagram: Classification of Phase Portaits
     in the $(det A,Tr A)$-plane}}] {};
  node at (+x) [label={[right,yshift=-0.5ex]$scriptstyleTr A$}] {}; 
  node at (+y) [label={[above]$scriptstyledet A$}] {};
  node at (-4,4) [pin={[above]$scriptstyleDelta=0$}] {};
  node at ( 4,4) [pin={[above,align=left]{%
    $scriptstyleDelta=0$:
    $scriptstyledet A=frac{1}{4}(Tr A)^2$}}] {};
  % inlays
  node at (0,-1.4) {inlaysaddle};
  node at (0,1.2)
    [pin={[draw,right,xshift=0.3cm]inlaycentre}] {};
  node at (0,0)
    [pin={[draw,above left,align=center,xshift=-0.3cm]%
    inlaycaption{uniform}[-1ex]inlaycaption{motion}}] {};
  node at (-4,1) {inlaysink};
  node at ( 4,1) {inlaysource}; 
  node at (-3,0) [pin={[draw,below,yshift=-1cm]inlaystablefp}] {};
  node at  (3,0) [pin={[draw,below,yshift=-1cm]inlayunstablefp}] {};
  node at (-1.8,3.7) {inlayspiralsink};
  node at ( 1.8,3.7) {inlayspiralsource};
  node at (-3.5,{0.25*3.5*3.5})
    [pin={[draw,left,xshift=-1.15cm,yshift=-0.3cm]inlaydegensink}] {};
  node at ( 3.5,{0.25*3.5*3.5})
    [pin={[draw,right,xshift=0.9cm,yshift=-0.3cm]inlaydegensource}] {};
end{tikzpicture}
end{document}

I tried to edit the code to create two other distinct phase portrait, but I couldn’t quite understand the code.

I was trying to create, for example, this phase portrait,

I would like to understand the code and how to create these examples.