\documentclass{standalone}
\usepackage{tikz,amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    axis lines=middle,
    xlabel={$N$},
    ylabel style={align=center},
    ylabel={$\omega = \dfrac{N\phi(N,P)}{P}$},
    xtick=\empty, ytick=\empty,
    xmin=0, xmax=10,
    ymin=0, ymax=1.2,
    width=13cm,
    height=8cm,
    domain=0:10,
    samples=300,
    axis line style={->},
    clip=false
]

% Tham số
\def\gamma{1}
\def\A{5}

% Type 1: gamma * N (tuyến tính)
\addplot [black, thick, domain=0:10] {0.3 * x}
    node[pos=0.97, anchor=west] {\small $\gamma N$ \\[-2pt] \footnotesize type 1};

% Type 2: gamma*N / (A + N)
\addplot [black, thick, domain=0:10] {\gamma*x / (\A + x)}
    node[pos=0.7, anchor=west] {\small $\dfrac{\gamma N}{A + N}$ \\[-2pt] \footnotesize type 2};

% Type 3: gamma*N^2 / (A^2 + N^2)
\addplot [black, thick, domain=0:10] {\gamma*x^2 / (\A^2 + x^2)}
    node[pos=0.42, anchor=south east] {\small $\dfrac{\gamma N^2}{A^2 + N^2}$ \\[-2pt] \footnotesize type 3};

% Đường gạch ngang tại y = gamma
\draw[dashed] (axis cs:0,1) -- (axis cs:10,1);
\node[anchor=west] at (axis cs:0.3,1.05) {\footnotesize $\gamma$ (max feeding rate)};

\end{axis}
\end{tikzpicture}
\end{document}
