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

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Akhtar Jan on 19 Dec 2021
Commented: Rena Berman on 25 Jan 2022
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 on 25 Jan 2022

Walter Roberson on 19 Dec 2021
Edited: Walter Roberson on 19 Dec 2021
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
##### 2 CommentsShowHide 1 older comment
Akhtar Jan on 19 Dec 2021
Is this is the correct Phase Portrait?