kuramoto matlab code:

function kuramoto(N)

if nargin

N=100;

end

% timesteps

ts=100;

show=1;

% visualization

% 1 = circle, 2 = square

viz=2;

% only change the two parameters below

K=0.2; % can try multiple K values by setting K as a vector

sigma=.3;

% timestep

dt=1; % seconds

%initialize

w=randn(N,1)*sigma + 1;

th0=randn(N,1)*.2;

rc=zeros(1,ts);

figure(1); gcf;

clf;

set(gcf, 'units', 'normalized');

set(gcf, 'position', [0.1479 0.6947 0.4974 0.2079]);

for Ki=K

[t, th]=ode45(@kuramoto_ode, 0:dt:ts, th0, [], w, Ki);

th=th';

th1=-pi:.1:pi;

for k=2:numel(t)

rc(Ki==K,k)=1/N*norm([sum(cos(th(:,k))), sum(sin(th(:,k)))]);

if show

subplot(1,2,1); gca; cla;

% the multiplier just verifies that everything is okay

if viz==2

vals=mod(th(:,k), pi);

A=ones(sqrt(N)).*reshape(vals,sqrt(N),sqrt(N))*255/pi;

imshow(uint8(A));

elseif viz==1

plot(cos(th(:,k)), sin(th(:,k)), 'ko');

hold on;

plot(cos(th1), sin(th1), 'b');

end

subplot(1,2,2); gca; cla;

% psi=mean(th(:,k));

plot(1:k, rc(1:k), 'k'); hold on;

xlabel('time');

ylabel('coherence');

drawnow;

box off;

end

end

end

plot(rc', 'linewidth', 2); hold on;

for jj=1:size(rc,1)

text(k+5, rc(jj,end), sprintf('%.2f', K(jj)), 'fontsize', 16);

end

set(gca, 'fontsize', 16);

xlabel('time (s)');

set(gca, 'xticklabel', get(gca, 'xtick')*dt);

ylabel('coherence');

function xdot=kuramoto_ode(t,x, w, K)

N=numel(w);

for i=1:N

xdot(i,1)=w(i) + K/N*sum(sin(x-x(i)));

end

. Simulate synchronization in networks using the Kuramoto model (use MATLAB code kuramoto.m). Note that beyond a certain coupling strength, the oscillators start to synchronise. This threshold value is called the critical coupling. Using simulations determine the critical coupling Ke when the natural frequencies of the coupled oscillators are sampled from a normal distribution with mean as 1 Hz and standard deviation as 0.3. 5] . Simulate synchronization in networks using the Kuramoto model (use MATLAB code kuramoto.m). Note that beyond a certain coupling strength, the oscillators start to synchronise. This threshold value is called the critical coupling. Using simulations determine the critical coupling Ke when the natural frequencies of the coupled oscillators are sampled from a normal distribution with mean as 1 Hz and standard deviation as 0.3. 5]