I am plotting the logistic growth model using ode45,But I am confused because I am getting oscillation while I should get a constant line so do you think there is another routine could I use it or I need to change something to get the right plot??

The model is :

dxdt=N0*x*(1-x/k)

What I am doing is :

tspan=0:0.001:100;

x0=0.1;

[t,x]=ode45('funname',tspan,x0)

figure

plot(t,x)

[Ced]

Looks alright to me. Your time-step is probably unnecessarily small, but that's up to you. Can you post your complete code?

However, most likely it's just due to your choice of "k".

[Rick Rosson]

What are the values of N0 and k?

[Avan Al-Saffar]

function Runlogisticconstant1

p0=0.1;

tspan=0:0.001:100;

K=10;

N0=1;

[t,p]=ode45(@logisticconstant,tspan,p0,[],N0,K);

plot(t,p)

1;

% function dpdt = logisticconstant(t,p,N0,K)

% dpdt= N0*p*(1-p./K);

% end

Answer 1

[Matt Tearle]

The oscillation you're seeing is a standard numerical artifact that comes from using an explicit RK method. (Look at the scale of the oscillation -- it's small.) The solution to the ODE settles very quickly to equilibrium, which causes stability issues for a numerical solver (it's very easy to overshoot the solution, then have to come back, overshoot again, etc., which is the behavior you're seeing).

Check the doc for ode45 to see the other solvers that are available. A stiff solver such as ode23s will give you better behavior (as far as the oscillation is concerned, at least).

[Matt Tearle]

With the values of K and N0 you gave in your comment, I got pretty nice results with ode23s and ode15s right off the bat. You can do even better by just requiring tighter tolerances:

p0=0.1;
tspan=0:0.001:100;
K=10;
N0=1;
[t,p]=ode23s(@(t,p) N0*p*(1-p./K),tspan,p0,odeset('AbsTol',1e-8,'RelTol',1e-10'));
plot(t,p)

(Takes about 1.5 seconds to run on my machine.)

But tighter tolerances also help with ode45. Using the above settings, the oscillation is still there, but it's barely noticeable.