Latex help to draw bifurcation diagram

I hope this helps:

documentclass[tikz]{article}
usepackage{tikz}
usetikzlibrary{plotmarks}

begin{document}    
    begin{tikzpicture}
        
        draw[] (-1, -3) -- (-1, 3) node[above] {};
        draw[] (-2, -0.5) -- (5, -0.5) node[right] {C};
        draw[] (0, -3) -- (0, 3) node[above] {};
        draw[] (1, -3) -- (1, 3) node[above] {};
        draw[] (2, -3) -- (2, 3) node[above] {P};
        draw[] (3, 3) -- (3, -3) node[below] {$ C=frac{kN}{4} $};
        draw[] (4, -3) -- (4, 3) node[above] {};

        draw[scale=0.5, domain=-3:3, smooth, variable=y,cyan,thick]  plot ({(-y*y)+4}, {y});
        
        %plotmarks
        node[cyan] at (-1,0) {pgfuseplotmark{triangle*}};
        node[cyan] at (0,0) {pgfuseplotmark{triangle*}};
        node[cyan] at (1,0) {pgfuseplotmark{triangle*}};
        node[cyan,rotate=60] at (3,0) {pgfuseplotmark{triangle*}};
        node[cyan,rotate=60]at (4,0) {pgfuseplotmark{triangle*}};
        
        node[cyan,rotate=60] at (-1,1.6) {pgfuseplotmark{triangle*}};
        node[cyan,rotate=60] at (0,1.4) {pgfuseplotmark{triangle*}};
        node[cyan,rotate=60] at (1,1.1) {pgfuseplotmark{triangle*}};
        node[cyan,rotate=60] at (2,0.7) {pgfuseplotmark{triangle*}};
        
        node[cyan] at (-1,-1.6) {pgfuseplotmark{triangle*}};
        node[cyan] at (0,-1.4) {pgfuseplotmark{triangle*}};
        node[cyan] at (1,-1.1) {pgfuseplotmark{triangle*}};
        node[cyan] at (2,-0.7) {pgfuseplotmark{triangle*}};   
        
    end{tikzpicture}
end{document}