how to add arrow on phase portrait

I still have some difficulties to add the arrowheads nicely on the curved trajectories. With dynamics on the script is now fixed, you may post a new question on the arrowhead plotting issue . i want output like this but i still have no arrow code

to    =  0;
tf    = 30;
tspan = to:0.1:tf;

iv1 = [ 12.3 0.1 0 0.1 0.1 ] ;
[t y] = ode45(@(t, y) lnear(t, y), tspan, iv1);
plot(y(:,1), y(:,5)), hold on

iv2 = [ 12.3 0 0 0 0 ] ;
[t x] = ode45(@(t, x) lnear(t, x), tspan, iv2);
plot(x(:,1), x(:,5)), 

iv3 = [ 12.65 0 0 0.1 0.1 ] ;
[t z] = ode45(@(t, z) lnear(t, z), tspan, iv3);
plot(z(:,1), z(:,5)), 

iv4 = [ 12.65 0.1 0.1 0 0 ] ;
[t n] = ode45(@(t, n) lnear(t, n), tspan, iv4);
plot(n(:,1), n(:,5)), 

iv5 = [ 12.485594 0 0 0 0.12 ] ;
[t w] = ode45(@(t, w) lnear(t, w), tspan, iv5);
plot(w(:,1), w(:,5)), 

iv6 = [ 12.3 0.1 0 0.1 0 ] ;
[t v] = ode45(@(t, v) lnear(t, v), tspan, iv6);
plot(v(:,1), v(:,5)), 

iv7 = [ 12.4 0.05 0 0.05 0 ] ;
[t s] = ode45(@(t, s) lnear(t, s), tspan, iv7);
plot(s(:,1), s(:,5)), 

iv8 = [ 12.65 0.05 0 0.05 0.05 ] ;
[t p] = ode45(@(t, p) lnear(t, p), tspan, iv8);
plot(p(:,1), p(:,5)), 

iv9 = [ 12.6 0.05 0 0.05 0 ] ;
[t c] = ode45(@(t, c) lnear(t, c), tspan, iv9);
plot(c(:,1), c(:,5)), grid on

xlabel('y_1'), ylabel('y_5')

function dydt = lnear(t,y)
    dydt = zeros(5, 1);
    e1 = 13;
    g  = 0.0125;
    h  = 0.284253;
    f  = 0.05;
    q1 = 0;
    k1 = 10;
    d1 = 0.0412;
    e2 = 0.0188;
    j  = 0.0082;
    q2 = 0;
    k2 = 10;
    d2 = 0.0288;
    b  = 2;
    d4 = 0.1152;
    e3 = 0.166667;
    a  = 1.7;
    q3 = 0;
    k3 = 10;
    d3 = 0.1152;
    r  = 0.5;
    m  = 1.02;
    q4 = 0;
    k4 = 10;
    dydt(1) = e1 + (g*y(3)*y(1)/(h + y(3))) + (f*y(3)*y(1)) - (y(1)*(1 + ((q1/k1)*y(1)))) - (d1*y(1));
    dydt(2) = e2*y(2) + (f*y(1)*y(3)) - (j*y(2)) - (y(2)*(1 + ((q2/k2)*y(2)))) - (d2*y(2));
    dydt(3) = (b*e2*y(2)) - (d4*y(3));
    dydt(4) = e3*y(4) + (j*y(2)) - (a*y(4)) - (y(4)*(1 + ((q3/k3)*y(4)))) - (d3*y(4));
    dydt(5) = (r*y(5)*(1 - (m*y(5)))) + (a*y(4)) - y(5)*(1 + ((q4/k4)*y(5)));
end

Answer 1

[Star Strider]

Use the quiver function —

to    =  0;
tf    = 30;
tspan = to:0.1:tf;

plotArrows = @(m) quiver(m(:,1), m(:,5), gradient(m(:,1)), gradient(m(:,5)));

figure
iv1 = [ 12.3 0.1 0 0.1 0.1 ] ;
[t y] = ode45(@(t, y) lnear(t, y), tspan, iv1);
plotArrows(y), hold on

iv2 = [ 12.3 0 0 0 0 ] ;
[t x] = ode45(@(t, x) lnear(t, x), tspan, iv2);
plotArrows(x), 

iv3 = [ 12.65 0 0 0.1 0.1 ] ;
[t z] = ode45(@(t, z) lnear(t, z), tspan, iv3);
plotArrows(z), 

iv4 = [ 12.65 0.1 0.1 0 0 ] ;
[t n] = ode45(@(t, n) lnear(t, n), tspan, iv4);
plotArrows(n), 

iv5 = [ 12.485594 0 0 0 0.12 ] ;
[t w] = ode45(@(t, w) lnear(t, w), tspan, iv5);
plotArrows(w), 

iv6 = [ 12.3 0.1 0 0.1 0 ] ;
[t v] = ode45(@(t, v) lnear(t, v), tspan, iv6);
plotArrows(v), 

iv7 = [ 12.4 0.05 0 0.05 0 ] ;
[t s] = ode45(@(t, s) lnear(t, s), tspan, iv7);
plotArrows(s),

iv8 = [ 12.65 0.05 0 0.05 0.05 ] ;
[t p] = ode45(@(t, p) lnear(t, p), tspan, iv8);
plotArrows(p),

iv9 = [ 12.6 0.05 0 0.05 0 ] ;
[t c] = ode45(@(t, c) lnear(t, c), tspan, iv9);
plotArrows(c), grid on

xlabel('y_1'), ylabel('y_5')

function dydt = lnear(t,y)
    dydt = zeros(5, 1);
    e1 = 13;
    g  = 0.0125;
    h  = 0.284253;
    f  = 0.05;
    q1 = 0;
    k1 = 10;
    d1 = 0.0412;
    e2 = 0.0188;
    j  = 0.0082;
    q2 = 0;
    k2 = 10;
    d2 = 0.0288;
    b  = 2;
    d4 = 0.1152;
    e3 = 0.166667;
    a  = 1.7;
    q3 = 0;
    k3 = 10;
    d3 = 0.1152;
    r  = 0.5;
    m  = 1.02;
    q4 = 0;
    k4 = 10;
    dydt(1) = e1 + (g*y(3)*y(1)/(h + y(3))) + (f*y(3)*y(1)) - (y(1)*(1 + ((q1/k1)*y(1)))) - (d1*y(1));
    dydt(2) = e2*y(2) + (f*y(1)*y(3)) - (j*y(2)) - (y(2)*(1 + ((q2/k2)*y(2)))) - (d2*y(2));
    dydt(3) = (b*e2*y(2)) - (d4*y(3));
    dydt(4) = e3*y(4) + (j*y(2)) - (a*y(4)) - (y(4)*(1 + ((q3/k3)*y(4)))) - (d3*y(4));
    dydt(5) = (r*y(5)*(1 - (m*y(5)))) + (a*y(4)) - y(5)*(1 + ((q4/k4)*y(5)));
end

Make appropriate changes to get the result you want.

.