Plotting 3D graph with ODEs

Hello there, I am looking for a possible way to plot 3D surface/graphs/plot from the data set I get from a system of ODEs that I created and solved using ode45, but I am unsure of how to get it.

Lets say I have the function files of the system of ODEs,and each time I run, I manipulate the parameters one by one to see their effect on the ans I get. For eg, I started off with the parameter A=0, and B = 3, which allows me to get population(t). Then I changed one of the parameter each time, A = 0, 20, 40, 60, 80 100 respectively. For each value of A, I also changed the B= 3, 6, 9, 12. respectively. Isit possible for me to plot a combined 3D plot of A, B and the population(t) and is there a better way/less tedious way to program this? If so, what is the suggested steps that I should take or do?

Thanks in advance!

Answer 1

[J. Alex Lee]

If your ODE result "population(t)" a scalar value, then yes, you can use surf() if your [A,B] is defined using meshgrid.

[Clement Koh]

I see. In this case, I can meshgrid [A,B] where A=[0:20:100] & B=[3 6 9 12]? How do I form my matrix for population(t) given that i have so many of it.

[J. Alex Lee]

[A,B] = meshgrid((0:20:100),(3:3:12))

PT = nan(size(A)); % preallocate
for k = 1:numel(A)
    PT(k) = % whatever number to extract from your ODE solution
end

Does it help?

If you are saying "population(t)" is actually a list of values, not just a number, then you should think harder about what it means to draw the plot you are thinking of.

[Clement Koh]

Thanks!

In general, I would want to find out whats the population at every point of time when the value of A and B changes. Not sure how I could change my code below

Currently this is my code:

%Main
to = 0;
tf = 365;
tspan = to:1:tf;
y0 = [1000000 100];

[t1,Y1] = ode45(@Sub_3D_plot_1, tspan, y0);

A=[0 20 40 60 80 100];
B=[3 6 9 12];
z = ;%Trying to form this with results from dYdt(2) in the function file whenever A and B changes

[X,Y] = meshgrid(A,B);
surf(X,Y,z)

Here is my part of my function file:

function dYdt = Sub_3D_plot_1(t,Y)

for A =0:20:100
    for B= 90:90:360  
b = 1/B;
C = 10;
dYdt(1) = -(C*Y(1))+(b*(1+3));
dYdt(2) = (C*Y(1))-(0.02*Y(2));
    end
end
end

[J. Alex Lee]

In a 3D plot, you have available 3 coordinates, x,y,z. You are using up (x,y) with your A and B values. You can represent a "point" at that (x,y) with another single value z. How do you expect a plot to look if you want multiple values of z stacked onto each other at that single (x,y)? Even if you did do that, how would you interpret the interrelation among those multiple stacked points (their relation in time, e.g.)?

[Clement Koh]

Alright, thanks for the input!