Plotting 3d ODE

I have to following code designed to plot and ODE system of 3 variables with respect to t.

t_start = 0; t_end = 50000;  %set suitable time range
t_duration = [t_start t_end];   %create vector for time

[w(:,1), w(:,2), w(:,3)] = meshgrid([-1:0.1:1;],[-1:0.1:1;], [-1:.1, 1]); %create grid
w_initial = [-1; .1; -.1];          %column vector containing initial values
[t, w] = ode23(@thefunc, t_duration, w_initial);
surf(w(:,1),w(:,2), w(:,3));

function wdot = thefunc(t, w)
a = .5;
b = .4;
c = -.75;
c_0 = -1;
A = .5; %greek variable alpha
wdot = zeros(3, 1);
wdot = [a*w(2)*w(3) - A*w(1).^3; 
        b*w(3)*w(1) - A*w(2).^3;
        c*w(1)*w(2) + w(1)*w(2) - A*w(3) - w(1)*w(2)*(-c_0.^2*b*w(1) - c_0.^2*a*w(2).^2 + c_0*A*w(1)^2 + c_0*A*w(2).^2 - c_0*A+ c)];
end

I get the error message Unable to perform assignment because the size of the left side is 9977-by-1 and the

size of the right side is 21-by-21-by-3. in the line with the meshgrid, and I'm not sure how to fix it.

Answer 1

[Star Strider]

First, delete the meshgrid call, since it is not necessary here. The ode23 call produces vectors, not a surface.

Second, plot this instead:

figure
stem3(w(:,1),w(:,2), w(:,3), '.');
grid on
xlabel('w_1(t)')
ylabel('w_2(t)')
zlabel('w_3(t)')

The stem3 plot gives a bit more information than plot3 would.

.

[Star Strider]

UPDATE — (2 Oct 2021 at 10:46)

With the online Run feature now enabled (not available until June 2021), the code becomes —

t_start = 0; t_end = 50000;  %set suitable time range
t_duration = [t_start t_end];   %create vector for time

w_initial = [-1; .1; -.1];          %column vector containing initial values
[t, w] = ode23(@thefunc, t_duration, w_initial);

figure
stem3(w(:,1),w(:,2), w(:,3), '.');
grid on
xlabel('w_1(t)')
ylabel('w_2(t)')
zlabel('w_3(t)')

function wdot = thefunc(t, w)
a = .5;
b = .4;
c = -.75;
c_0 = -1;
A = .5; %greek variable alpha
wdot = zeros(3, 1);
wdot = [a*w(2)*w(3) - A*w(1).^3; 
    b*w(3)*w(1) - A*w(2).^3;
    c*w(1)*w(2) + w(1)*w(2) - A*w(3) - w(1)*w(2)*(-c_0.^2*b*w(1) - c_0.^2*a*w(2).^2 + c_0*A*w(1)^2 + c_0*A*w(2).^2 - c_0*A+ c)];
end

With the desired 3D plot.

.