webdiagram-logistic

\documentclass[]{standalone}

\usepackage[]{graphicx}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\tikzset{>=latex}
\usetikzlibrary{arrows,arrows.meta}
\usepackage{steinmetz}
\newcommand*{\equal}{=}

\usepackage{tikz-3dplot}
\usetikzlibrary{decorations.markings}

\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{>}}},postaction={decorate}}}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    width=7cm,height=7cm,
    xmin=0,xmax=1,
    ymin=0,ymax=1,
    grid=both,
    %grid style={line width=.1pt, draw=gray!10},
    major grid style={line width=.3pt,draw=gray!70},
    axis lines=middle,
    %minor tick num=5,
    xtick = {0,1/2, 1},
    ytick = {0, 1/2,1},
%    xticklabels={$-\sqrt{3}$, $0$, $\sqrt{3}$},    
%    yticklabels={$-\sqrt{3}$, $0$, $\sqrt{3}$},    
    enlargelimits={abs=0.05},
    ticklabel style={font=\tiny},
    xlabel={$x$},
    ylabel={$y$},
    xlabel style={font=\tiny, at={(ticklabel* cs:1)},anchor=north},
    ylabel style={font=\tiny, at={(ticklabel* cs:1)},anchor=west},
    ]
    \draw (axis cs:0,0) node[below=4pt,left=0pt] {\tiny$0$};
    \addplot[domain=0:1,samples=100] {7*(x-x^2)/4};
    \addplot[domain=0:1,samples=10] {x} ;
     \fill (axis cs:3/7,3/7) circle [radius=0.02];
	\draw [thick, ->-=0.5] (0.95,0.083125) -- (0.083125,0.083125) -- (0.083125,0.133377) -- 
(0.133377,0.133377) -- (0.133377,0.202278) -- (0.202278,0.202278);
	\draw [thick, ->-=0.5] (0.202278,0.202278) --
(0.202278,0.282383) -- (0.282383,0.282383) -- (0.282383,0.354625) -- 
(0.354625,0.354625) -- (0.354625,0.400516) -- (0.400516,0.400516) -- 
(0.400516,0.42018) -- (0.42018,0.42018) -- (0.42018,0.42635) --
(0.42635,0.42635) -- (0.42635,0.428008) -- (0.428008,0.428008);
\draw[thick,->-=0.5] (0.5,0.4375) -- (0.4375,0.4375) -- (0.4375,0.430664) -- 
(0.430664,0.430664);
  \end{axis}
 \end{tikzpicture}

\end{document}