phase portrait mathematical modelling

I have problem about mathematical modelling , can you help me fix this script matlab i attach with , didn't run.

this is output i want

Answer 1

[Sam Chak]

Hi @Latifah

I think there is one unreadable non-ANSI character (probably a math operator sign) in the lnear.m file.

I replaced that character with a plus sign. Please check the equations if they are absolutely correct.

Edit: The script is now fixed and Oil Palm tree pattern is basically plotted. However, to add a few arrowheads on the curved trajectories is slightly challenging to me. Try checking out the examples in the FileExchange to see if you can use some arrow functions there:

https://www.mathworks.com/matlabcentral/fileexchange/116840-matlab-diagrams

Some MVP experts in graphics and advanced plotting maybe able to help you.

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

[Latifah]

thank you , how can I get lots of arrows and directions like the picture I attached?

[Latifah]

I've changed my script, but haven't got the results that match the picture, namely the collection of all directions and arrows, can you help me again?

clc; clear
figure1=figure;
axes1=axes('Parent',figure1,'FontSize',13);
grid on;
box(axes1,'on');
hold(axes1,'all');
to = 0 ;
tf = 30;
tspan = to : 0.001 : tf ;
iv = [ 12.3 0.1 0 0.1 0.1 ] ;
iv2 = [ 12.3 0 0 0 0 ] ;
iv3 = [ 12.65 0 0 0.1 0.1 ] ;
iv4 = [ 12.65 0.1 0.1 0 0 ] ;
iv5 = [ 12.485594 0 0 0 0.12 ] ;
iv6 = [ 12.3 0.1 0 0.1 0 ] ;
iv7 = [ 12.4 0.05 0 0.05 0 ] ;
iv8 = [ 12.65 0.05 0 0.05 0.05 ] ;
iv9 = [ 12.6 0.05 0 0.05 0 ] ;
[t y] = ode45(@(t, y) lnear(t, y), tspan, iv);
[t x] = ode45(@(t, x) lnear(t, x), tspan, iv2);
[t z] = ode45(@(t, z) lnear(t, z), tspan, iv3);
[t n] = ode45(@(t, n) lnear(t, n), tspan, iv4);
[t w] = ode45(@(t, w) lnear(t, w), tspan, iv5);
[t v] = ode45(@(t, v) lnear(t, v), tspan, iv6);
[t s] = ode45(@(t, s) lnear(t, s), tspan, iv7);
[t p] = ode45(@(t, p) lnear(t, p), tspan, iv8);
[t c] = ode45(@(t, c) lnear(t, c), tspan, iv9);
plot(y(:,1), y(:,5)), grid on
plot(x(:,1), x(:,5)), grid on
plot(z(:,1), z(:,5)), grid on
plot(n(:,1), n(:,5)), grid on
plot(w(:,1), w(:,5)), grid on
plot(v(:,1), v(:,5)), grid on
plot(s(:,1), s(:,5)), grid on
plot(p(:,1), p(:,5)), grid on
plot(c(:,1), c(:,5)), grid on
plot(12.485594+0*tspan,0+0*time,'k*','LineWidth',10)
xlabel('y_1'), ylabel('y_5')

[Sam Chak]

Hi @Latifah

I have edited to show the Oil Palm pattern trajectories. But 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. Hope the Graphic Experts can help out.

[Latifah]

okay thankyou so much . I'm very helped