CDS - Lecture 9 ~ Matlab Script 'flow1D_ode'

• Source: moodle

function flow1D_ode()
    
    %
    % Draw the flow of a 1D system
    %
    
    close all
    
     Define the x and y sets
    xmin = -5;
    xmax = +5;
    x = linspace(xmin, xmax, nPoints);    
    
     Evaluate the derivative
    dx = -10*x + x.^3;
    
     Draw the flow
    hold on
    h = quiver(x, 0*x, dx, 0*dx, 'b');
    
     Draw the steady states
    plot(x1, 0, 'ro')
    plot(x2, 0, 'ro')
    plot(x3, 0, 'ro')
    
     Evaluate the solution
    x0 = 0.1; % Initial condition
    T = 1; % Time horizon
    [t, x] = ode45(@f, [0, T], x0); % Solve!
    
    %% Draw the solution
    figure
    plot(t, x)
    xlabel('t')
    ylabel('x(t)')
end
    
function dx = f(t, x)
    dx = -10*x + x^3;
end