How to solve non linear system of ODE about trophic levels?
1 view (last 30 days)
Show older comments
Hi,
I have to solve this system of ODE in Matlab, describing nitrogen exchanges between different trophic levels.
The problem is that I am not satisfied by the plot, I expected something different according to Lotka_Volterra equations.
I Include the script, the function, the plot and the text of the exercise.
Thaks for any advice,
C.
global r K p1 p2 rho1 rho2 rho3 rho4 mu1 mu2 mu3 mu4 l1 l4 k50 F05y U F05t
r=0.1;
K=20000;
p1=0.1;
p2=0.05;
rho1=0.6;
rho2=0.6;
rho3=0.6;
rho4=0.6;
mu1=0.2;
mu2=0.4;
mu3=0.5;
mu4=0.6;
l1=0.05;
l4=0.1;
k50=0.3;
U=13*10.^12;
F05t=(linspace(0,20,200)); % external time dependent input for the fifth equation
F05y=zeros(1,200);
F05y(1:end)=U;
Y0=[200, 100, 50, 50, 500]; %condizioni iniziali
t0=0;
tf=20;
tRange=[t0,tf]; %intervallo di tempo
%ode45
[tSol,YSol]=ode45(@prede_predatoriCopia, tRange, Y0); %runge kutta 4-5 ordine
passiode45=length(tSol)
y1=YSol(:,1);
y2=YSol(:,2);
y3=YSol(:,3);
y4=YSol(:,4);
y5=YSol(:,5);
figure
plot(tSol,y1,'*'), hold on
plot(tSol,y2,'*')
plot(tSol,y3,'*')
plot(tSol,y4,'*')
plot(tSol,y5,'*'), hold off
legend('y1','y2','y3','y4','y5')
%%
function [dYdt] = prede_predatori(t,Y)
global r K p1 p2 rho1 rho2 rho3 rho4 mu1 mu2 mu3 mu4 l1 l4 k50 F05y F05t
y1=Y(1); %primar producers
y2=Y(2); %herbivorous
y3=Y(3); %carnivores
y4=Y(4); % decomposers
y5=Y(5); % nutritious
% F05=zeros(size(y1));
% F05(1000:end)=U;
F05=interp1(F05t,F05y,t);
dy1dt=r*y1*(1-y1/K)-p1*y1*y2-(rho1+mu1)*y1;
dy2dt=p1*y1*y2-(rho2+mu2)*y2-p2*y2*y3;
dy3dt=p2*y2*y3-(rho3+mu3)*y3;
dy4dt=mu1*y1+mu2*y2+mu3*y3-(rho4+mu4)*y4;
dy5dt=F05-l1*r*y1*(1-y1/K)+l4*mu4*y4-k50*y5;
dYdt=[dy1dt;
dy2dt;
dy3dt;
dy4dt;
dy5dt];
end
0 Comments
Answers (1)
Nikhil Sonavane
on 22 Dec 2020
You may refer to the following documentation to understand solving non-linear ODEs-
0 Comments
See Also
Categories
Find more on Ordinary Differential Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!