Drawing phase plane diagram of a system of 3 coupled odes - MATLAB

I have a system of 3 coupled odes and this is how I solve the system.

Tend = 100;
Nt = 100;
% Define RHS functions
RHS = @(t,x)RHS(t,x,param); 
%Execution-----------------------------------------------------------------
x0 = [0.004, 0.05, 0.1]; %Initial condition
t = linspace(0,Tend,Nt); %TSPAN
% Options with event function
[t, A] = ode45(RHS, t, x0);

I'd like to plot the phase plane diagram with the vector field for the solution of this model. I used quiver3 to create arrows for the system as follows:

N=20;        %number of arrows along each dimension

%Next: Compute N evenly spaced points along each axis.
xvals=linspace(min(A(:,1)),max(A(:,1)),N);
yvals=linspace(min(A(:,2)),max(A(:,2)),N);
zvals=linspace(min(A(:,3)),max(A(:,3)),N);

%Next: Make vectors of length N^3 that contain the x,y,z locations of all the arrows.
[X,Y,Z]=meshgrid(xvals,yvals,zvals);  %creates NxNxN arrays

%Next: Make X,Y,Z row vectors, since quiver3() won't accept NxNxN array.
X=reshape(X,1,N^3);
Y=reshape(Y,1,N^3);
Z=reshape(Z,1,N^3);
U=zeros(1,N^3); V=U; W=U;  %pre-allocate arrays U,V,W

for i=1:N^3
    %Next: Compute the direction components [U,V,W] for each arrow.
    deriv=RHS(0,[X(i),Y(i),Z(i)]);
    U(i)=deriv(1); V(i)=deriv(2); W(i)=deriv(3);
end

figure;
quiver3(X,Y,Z,U,V,W); %plot black arrows

This is the output of this code.

But I donot know how to plot the solution in this diagram as a surface or as trajectories to see the flow using arrows. Any help is much appreciated.

Answer 1

[Sam Chak]

Hi @UserCJ

I think you should be able to plot the trajectory solution using plot3 after retaining the 3D diagram (quiver3):

hold on
plot3(A(:,1), A(:,2), A(:,3))

or

hold on
plot3(sol(:,1), sol(:,2), sol(:,3))

[UserCJ]

Thanks @Sam Chak

I accidentally used "plot" instead of "plot3". Thanks for your suggestion.