kuramNetwork.asv

%% Run Kuramoto oscillator through network
function [theta,r, psi] = kuramNetwork (testNet,Edges,N,Lam,omega,theta,numNodes)
% This script  runs a kuramoto oscillator through a pre-generated network
% conditioned on local connections
% Numerical integration through fourth-order Runge-Kutta Method
% BC/ML/SWoNS/2018
% Code adapted from appmath.wordpress.com, courtesy
% Jeongho Kim, Mathematical Sciences, Seoul National University.
% Someone please clean

%% Generate network
iter = 250;
h = 0.1;
r = zeros(length(iter-1),1);

figure;
movegui('center');
for k = 1:iter-1
    
    thetaConnect = theta(:,k)*ones(1,N)-(ones(N,1)*theta(:,k)'); %Generates phase matrix\
    indEdgeConnect = adjacency(testNet);
    thetaConnect(~indEdgeConnect) = 0; %no connection == 0
        
        f1 = kuramoto (thetaConnect,Lam,N,omega);
        f2=kuramoto(thetaConnect+0.5*h*f1(:,1),Lam,N,omega);
        f3=kuramoto(thetaConnect+0.5*h*f2(:,1),Lam,N,omega);           %4-th order Runge-Kutta method.
        f4=kuramoto(thetaConnect+h*f3(:,1),Lam,N,omega);        
        theta(:,k+1) = theta(:,k)+(h/6)*(f1(:,1))+2*f2(:,1)+2*f3(:,1)+f4(:,1);
        
        indOver = find (theta(:,k+1) > 2*pi);
        indUnder = find (theta(:,k+1) < 0);
        
        theta(indOver,k+1) = theta(indOver,k+1) - 2*pi;
        theta(indUnder,k+1) = theta(indUnder,k+1) + 2*pi;
        
        z = sum(exp(1i*theta(:,k+1)))/N;
        r(k+1) = abs (z);
        psi(k+1) = angle(z);
        if k == iter/2
            theta (:,k+1) = theta(:,k) .* randn(1,size(theta,1))'+50;
            pause(1)
        end
x=cos(theta(:,k));
y=sin(theta(:,k));

s=linspace(0,2*pi,100);
cx=cos(s);
cy=sin(s);
s = plot(x,y,'o',cx,cy);
set(s,'MarkerSize',20);
axis([-1 1 -1 1])
axis square
 
drawnow
        
end

function f=kuramoto(x,Lam,N,omega)
 
f=omega+(Lam/N)*sum(sin(x))'; %Take out rand for noise
 
end

end