MATLAB: How to draw a trajectory

chaosodetrajectory

Hi
i have a differential equation like this:
x'' + x + x^2 = 0
its a chaos problem and i want to display the trajectories.it has two fix point, a saddle at (-1,0) and a repellor at (0,0).
we can transform the equation to ODE by this:
x'= y
y'= -x -x^2

Best Answer

Mostafa, try something like
 function my_phase()
 IC = rand(10,2);
 hold on
 for ii = 1:length(IC(:,1))
    [~,X] = ode45(@EOM,[0 2],IC(ii,:));
    x = X(:,1);
    y = X(:,2);
    plot(x,y,'r')
 end
 xlabel('x')
 ylabel('y')
 grid
 end
 function dZ = EOM(t, z)
 dZ = zeros(2,1);
 x  = z(1);
 y  = z(2);
 dZ = [  y;...
       - x - x^2];
 end
You can use the IC vector to place the initial conditions to specifically show the dynamics around the fixed points.
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