physics-vanderpol_oscilator.tex

% https://latexdraw.com/phase-portrait-of-van-der-pol-oscillator/
\documentclass[border=0.2cm]{standalone}
 
\usepackage{pgfplots}
\pgfplotsset{compat = newest}
 
% Define arrow's style
\usetikzlibrary{decorations.markings}
 
% Arrow style
\tikzset{decorated arrows/.style={
    postaction={
        decorate,
        decoration={
            markings,
            mark=between positions 0 and 1 step 15mm with {\arrow[black]{stealth};}
            }
        },
    }
}
 
 
\begin{document}
\begin{tikzpicture}
 
    \begin{axis}[
        grid=both,
        grid style={dashed,red!20},
        xmin = -4, xmax = 4,
        ymin = -4, ymax = 4,
        width = \textwidth,
        height = 0.7\textwidth,
        xlabel = {$x$},
        ylabel = {$y$},
        title={Phase Portrait of Van Der Pol Oscillator},
        view = {0}{90},
    ]
    
    % Vector Field
    \addplot3[
        quiver = {
            u = {y/sqrt(y^2+(0.8*(1-x^2)*y-x)^2)},
            v = {(0.8*(1-x^2)*y-x)/sqrt(y^2+(0.8*(1-x^2)*y-x)^2)},
            scale arrows = 0.25,
            },
        -stealth,
        domain = -4:4,
        domain y = -4:4,
        lightgray] 
    {0};
    
    % Plot the Limit Cycle       
    \addplot[ultra thick, red, decorated arrows] file {./data/vanderpol.txt};
    
    \end{axis}
\end{tikzpicture}
 
\end{document}