ODE45 for phase trajectory plot

Hi, I'm new in Matlab.

I used in ODE45 code to find phase trajectory of the following equations:

when my initial conditions are 0,0,0 I run the code with these initial conditions but I don't get any point on the plot. This is the code I wrote:

f1=[0 0 1];
f = @(t,x) [1*x(1)+x(2)-x(1)*x(3);-x(1);-0.9*x(3)+(x(1)^2);];
x0 = [0;0;0];
dt= 0.001;
tspan= 0.1:0.45:10;
[t,x] = ode45(f,tspan,x0);
p%lot3(x(:,1),x(:,2),x(:,3), "o")



u = gradient(x(:,1));
v = gradient(x(:,2));
w = gradient(x(:,3));
quiver3(x(:,1),x(:,2),x(:,3),u,v,w, '-b')

grid on
title('Phase trajectory')
subtitle('g=0.9')

xlabel('x'), ylabel('y'), zlabel('z') 

this is the plot that comes out when my initial conditions are 0,0,0:

Is it possible that ODE45 is not suitable for my problem? Where am I wrong?

I would appreciate any help.

Answer 1

[Cris LaPierre]

With initial conditions [0,0,0], the results of ode45 are all zeros, so there are no gradients.

Consider adjusting your initial conditions.

f = @(t,x) [1*x(1)+x(2)-x(1)*x(3);-x(1);-0.9*x(3)+(x(1)^2);];
x0 = [0.1;0;0];
tspan= 0.1:0.45:10;
[t,x] = ode45(f,tspan,x0);
plot3(x(:,1),x(:,2),x(:,3), "o")
grid on

[linoy Ban David]

Hi Cris,

Thank you very much for your help! I appreciate it(=