# 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??

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Avan Al-Saffar on 22 Oct 2014
Commented: Matt Tearle on 23 Oct 2014
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)
Avan Al-Saffar on 23 Oct 2014
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

Matt Tearle on 22 Oct 2014
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 on 23 Oct 2014
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.