CDS - Lecture 9 ~ Matlab Script 'flow2D_ode'

• Source: moodle

function flow2D_ode()
    
    %
    % Draw the flow of a 2D system
    %
    
    close all
    
     Define the x and y sets
    xmin = -1;
    xmax = +4;
    x = linspace(xmin, xmax, nPoints);
    
    ymin = -2;
    ymax = +3;
    y = linspace(ymin, ymax, nPoints);
    
    [X, Y] = meshgrid(x, y);
    
     Draw the flow
    figure
    quiver(X, Y, dX, dY, 'b')
    
     Draw the nullclines
    nPoints = 100; % Increase the resolution for the nullclines
    x = linspace(xmin, xmax, nPoints);
    plot(x, 2*x-(1/2)*x.^2, 'k--')
    plot(x, (1/2)*x, 'k--')
    
     Draw the solution over time
    figure
    plot(t, x)
    hold on
    plot(t, y)
    xlabel('t')
    legend('x(t)', 'y(t)')
    
end
 
function du = f(t, u)
    x = u(1);
    y = u(2);
    
    dx = -4*x + x^2 + 2*y;
    dy = x - 2*y;
    
    du = [dx; dy];
end