Lotka Volterra with an additional parameter

3 views (last 30 days)
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.
Script Window:
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);
end

Accepted Answer

Star Strider
Star Strider on 25 Sep 2020
I cannot imagine how you got that code to work at all, considering that the function you call in ode45 is not the function you posted!
Try this:
tspan = linspace(0, 400, 100);;
P0 = [200, 50];
k = [-1, 1];
for k1 = 1:numel(k)
[t,P] = ode45(@(t,P)lotkawithk(t,P,k(k1)),tspan,P0);
Pm{k1} = P;
end
figure
hold on
for k1 = 1:numel(k)
plot(t,Pm{k1}(:,1), t,Pm{k1}(:,2), 'DisplayName',sprintf('k = %d',k(k1))) %This section gives me the error. It works, however, if I use t instead of k.
end
grid
legend
function [dPdt] = lotkawithk(t,P,k)
alpha = 1;
beta = 0.05;
gamma = 0.05;
delta = 0.0025;
x = P(1);
y = P(2);
dPdt = zeros(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);
end
Note that ‘k’ is passed as a parameter.
Make appropriate changes to get different results.
  6 Comments
Khushi Patel
Khushi Patel on 25 Sep 2020
Oh okay. Greatly appreciate the help and the clarification about plotting k!

Sign in to comment.

More Answers (1)

Khushi Patel
Khushi Patel on 25 Sep 2020
The equations are:

Categories

Find more on Line Plots 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!