Can someone help me implement my Kuramoto Model with time delay please?

Hi there,

I want to solve numerically a system of DDEs with two coupled oscillators based on the Kuramoto Model with a time delay. These are my DDEs:

where K is my coupling matrix. This is the code I am using but I keep getting that not enough inputs and it does not work:

N=2; % two oscillators: melatonin and cortisol

omega=2*pi; % intrinsic frequency of both oscillators: 24 hours

tau=[5*pi/9]; % time delay: 3 hours and 20 minutes

h=0.1; % step size

iter=500; % number of iterations

tspan=0:h:h*iter; % time

K=[0 0.5;0.5 0]; % initialising the coupling matrix

sol=dde23(@ddefun,tau,@history,tspan)

% Subfunctions

function dthetadt=ddefun(t,theta,Z,omega,K)

thetalag1=Z(:,1);

dthetadt=[omega+K(1,2)*sin(theta(2)-theta(1));

omega+K(2,1)*sin(thetalag1(1)-theta(2))];

end

function s=history(t)

s=ones(2,1);

end

Please can someone help me and see where I am going wrong?

Thank you.

Answer 1

[Fabio Freschi]

Your function requires additional parameters. One way to pass them is to use an anonymous function as extra layer

% params
N = 2; % two oscillators: melatonin and cortisol
omega = 2*pi; % intrinsic frequency of both oscillators: 24 hours
tau = 5*pi/9; % time delay: 3 hours and 20 minutes
h = 0.1; % step size 
iter = 500; % number of iterations 
tspan = 0:h:h*iter; % time
K = [0 0.5; 0.5 0]; % initialising the coupling matrix

% extra layer function so that omega and K are available to ddefun
myfun = @(t,theta,Z)ddefun(t,theta,Z,omega,K);

% call to solver
sol = dde23(myfun,tau,@history,tspan);

% Subfunctions
function dthetadt = ddefun(t,theta,Z,omega,K)
thetalag1 = Z(:,1);
dthetadt = [omega+K(1,2)*sin(theta(2)-theta(1));
    omega+K(2,1)*sin(thetalag1(1)-theta(2))];
end

function s = history(t)
s = ones(2,1);
end

You can find other strategies to pass extra parameters here

https://it.mathworks.com/help/optim/ug/passing-extra-parameters.html

[Newbie]

Thank you! It works.