Help with Matlab Homework: Lotka-Volterra Model

[jhox08]

Homework Statement

consider the Lotka-Volterra predator prey model defined by dx/dt=-0.1x+0.02xy and dy/dt=0.2y-0.025xy, x(t) is predators and y(t) is prey...us a numerical solver to graph x(t) and y(t)

Homework Equations

x(0)=6, y(0)=6

The Attempt at a Solution

here's my code, I honestly don't know if its right, but when I try to run it I get an error of Maximum recursion limit of 500 reached, can someone help me out with this, I'm not very good with Matlab, any advise would be great...thanks

function dp=pred(t,y)
clear;
g=0.2; d1=0.025; d2=0.1; c=0.02; y(1)=6; y(2)=6;
[T,Y]=ode45(@pred, [0,5],[6 6]);
dp=[g*y(1)-d1*y(1)*y(2); -d2*y(2)+c*y(1)*y(2)];
plot(T,Y(:,1),'-',T,Y(:,2),'--');

 

[KataKoniK]

legend('Predators','Prey');
xlabel('Time');
ylabel('Population');
title('Lotka-Volterra Predator-Prey Model');
end

Hi there,

Your code looks mostly correct, but there are a few things that could be causing the error you are seeing. First, you have defined your function "pred" inside the function "pred", which is not necessary. You can define your function outside of the ode45 function and then call it within the ode45 function.

Secondly, your initial conditions are being overwritten in the ode45 function. You don't need to define y(1) and y(2) within the function, as they are already defined as the initial conditions in the ode45 function.

Finally, your time span in the ode45 function is currently set to [0,5], which may not be long enough to capture the behavior of the predator-prey model. You may need to increase the end time to see the full dynamics.

Here is a revised version of your code that should work:

function dp=pred(t,y)
% Define parameters
g=0.2;
d1=0.025;
d2=0.1;
c=0.02;

% Define differential equations
dp=[g*y(1)-d1*y(1)*y(2); -d2*y(2)+c*y(1)*y(2)];

% Define initial conditions
y0 = [6;6];

% Define time span
tspan = [0,10];

% Solve differential equations
[T,Y]=ode45(@Pred, tspan, y0);

% Plot results
plot(T,Y(:,1),'-',T,Y(:,2),'--');
legend('Predators','Prey');
xlabel('Time');
ylabel('Population');
title('Lotka-Volterra Predator-Prey Model');
end

I hope this helps! Let me know if you have any further questions or if you would like me to explain any part of the code in more detail.