Coupled ODE Solver Producing Unexpected Graph

Incorrect graph generating with given code. Trying to solve a couped ODE problem. Thank you in advance.

clear;
clc;
 
t_initial=0;
t_final=800;
x0=500;
y0=200;
tSpan=[t_initial t_final];
v0=[x0 y0];
[t,v]=ode45(@ODEfun,tSpan,v0);
 
figure
plot(t,v(:,1),t,v(:,2));
legend('Fox','Rabbit');
xlabel('Time (days)');
ylabel('Population');
title('Rabbit and Fox Population Overtime');
 
 
function f=ODEfun(~,v)
x=v(1);
y=v(2);
k1=0.02;
k2=0.0004;
k3=0.00004;
k4=0.04;
dx_dt=(k1*x)-(k2*y);
dy_dt=(k3*x*y)-(k4*y);
f=[dx_dt;dy_dt];
end

[darova]

Here is what i got for t_final = 80

[VBBV]

I think you seem to get correct graph only for the given input conditions

Do you mean a graph like this below ?

Answer 1

[Pravin Jagtap]

Hello Brooke,

Please refer to following documentation for solving coupled system of ODEs

https://www.mathworks.com/help/symbolic/solve-a-system-of-differential-equations.html