I have attempted to model the equations provided below. the code keeps giving me an error when I try to plot the figure using the parameter k instead of t. I am trying to model the effect of varying k on the population dynamics for both prey and predator.
note: if I use plot(k, P) it gives me a complicated and entirely different graph that is unreadable.
tspan = [0, 400];
P0 = [200, 50];
k = [-1, 1];
[t,P] = ode45(@(t,P)lotkavolterra(t,P),tspan,P0);
plot(k,P(:,1),k,P(:,2)) %This section gives me the error. It works, however, if I use t instead of k.
function [dPdt] = lotkawithk(t,P)
alpha = 1;
beta = 0.05;
gamma = 0.05;
delta = 0.0025;
x = P(1);
y = P(2);
dPdt = zeroes(2,1);
dPdt(1) = alpha*x - (beta*x*y)/((log(exp(1)+t))^k);
dPdt(2) = (delta*x*y)/((log(exp(1)+t))^k) - (gamma*y);