Here we go,
t0 = 0;
tfinal = 15;
y0 = [20; 20]; % Initial conditions [prey, predator]
[t, y] = ode23(@lotka, [t0 tfinal], y0);
plot(t, y)
title('Predator/Prey Populations Over Time with Fixed Sum')
xlabel('Time')
ylabel('Population')
legend('Prey', 'Predator', 'Location', 'North')
function yp = lotka(t, y)
a = 1; % Growth rate of prey when there are no predators
b = 0.01; % Rate at which predators consume prey
c = 1; % Decay rate of predators when there are no prey
d = 0.02; % Rate at which predators increase by consuming prey
dpdt = a * y(1) - b * y(1) * y(2);
dqdt = -dpdt; % Making sure that the sum remains constant
yp = [dpdt; dqdt];
end
This will give you a plot where the sum of predators and prey remains constant at 40 (or whatever you set y0 to sum to). The populations will still oscillate, but in a manner constrained by this sum.
