How can I add Direction arrows in this Phase Portrait I mean arrows in the Direction of velocity

clear   
clc
clf
close all
k1 = 3;
k_1 = 1;
k2 = 3;
k3 = 0.6;
k_3 = 1;
k4 = 3;
f = @(t,a) [k_1*a(2)-k1*a(1)-k3*a(1)*a(2)-k_3*a(3);
    k1*a(1)-(k_1+k2)*a(2)-k3*a(1)*a(2)+(k4+k_3)*a(3);
    k3*a(1)*a(2)-(k4+k_3)*a(3)];
[t,a] = ode45(f,[0 100],[4.1 1.1 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
hold on
grid on
xlabel('S','fontsize',12)
ylabel('C1','fontsize',12)
zlabel('C2','fontsize',12)
[t,a] = ode45(f,[0 100],[4 1 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.9 .9 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.8 .8 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.7 .7 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.6 .6 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.5 .5 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.4 .4 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.3 .3 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.2 .2 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.1 .1 0]);     
plot3(a(:,1),a(:,2),a(:,3))
hold off

[Walter Roberson]

quiver() ?

[Akhtar Jan]

yes sir

[Akhtar Jan]

if you dont mind please run the code first

[Walter Roberson]

I cannot tell from the variable names which variables hold the velocity x and velocity y information. I am also not sure what variables hold the coordinates at which the components are to be plotted.

[Akhtar Jan]

Here x = a(1) = S, y = a(2) = C1 , Z = a(3) = C2 all the three are variables which are converging towards origin.

[Rik]

Original question content (the attached SC1C2best.m file can't be restored from Google cache):

clear   
clc
clf
close all
k1 = 3;
k_1 = 1;
k2 = 3;
k3 = 0.6;
k_3 = 1;
k4 = 3;
f = @(t,a) [k_1*a(2)-k1*a(1)-k3*a(1)*a(2)-k_3*a(3);
    k1*a(1)-(k_1+k2)*a(2)-k3*a(1)*a(2)+(k4+k_3)*a(3);
    k3*a(1)*a(2)-(k4+k_3)*a(3)];
[t,a] = ode45(f,[0 100],[4.1 1.1 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
hold on
grid on
xlabel('S','fontsize',12)
ylabel('C1','fontsize',12)
zlabel('C2','fontsize',12)
[t,a] = ode45(f,[0 100],[4 1 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.9 .9 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.8 .8 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.7 .7 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.6 .6 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.5 .5 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.4 .4 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.3 .3 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.2 .2 0]);     % Runge-Kutta 4th/5th order ODE solver
plot3(a(:,1),a(:,2),a(:,3))
[t,a] = ode45(f,[0 100],[3.1 .1 0]);     
plot3(a(:,1),a(:,2),a(:,3))
hold off

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Walter Roberson]

You cannot add velocity direction vectors to that plot, as none of your variables are velocity, and none of your variables allow velocity to be calculated (for example they are not acceleration.)

In order to plot velocity direction vectors, you need one of a small number of things:

1. x and y, or x and y and z components of the velocity at a series of x and y, or x and y and z locations
2. magnitude and direction components of the velocity at a series of x and y, or x and y and z locations
3. x and y, or x and y and z components of the velocity at a series of 2d polar or 3d spherical or 3d cylindrical coordinates
4. magnitude and direction components of the velocity at a series of 2d polar or 3d spherical or 3d cylindrical coordinates

[Akhtar Jan]

please check your inbox

[Akhtar Jan]

Is this is the correct Phase Portrait?