Created
November 12, 2013 14:22
-
-
Save jonathanBieler/7431596 to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
%Do the simulation and compute a few things from the traces | |
Ten = 24;%entrainement period | |
Tin = 12;%intrinsic period | |
m = @(th,t) 2*pi/Tin + 0.2*sin(th) * (0.5*cos( 2*pi/Ten*t) + 0.5)^10; | |
Nt = 1e5; | |
dt = 1e-2; | |
T = linspace(0,Nt*dt,Nt)'; | |
th = zeros(Nt,1); | |
th(1) = 2*pi*rand; | |
phi = 2*pi/Ten*T; | |
for t=1:Nt-1 | |
th(t+1) = th(t) + dt*m(th(t),dt*t); | |
end | |
%compute effective period : w = lim theta / t | |
weff = mean(th(end-1000:end)./T(end-1000:end)); | |
Teff = 2*pi/weff; | |
%is the phase difference growing like T ? | |
phaseDiffVsT = abs(th-phi)./T; | |
if( mean(phaseDiffVsT(end-100:end)) > 1e-2) | |
fprintf('\nNo 1:1 sychronization!\n') | |
else | |
fprintf('\n 1:1 Sychronization!\n') | |
end | |
phaseDiff = mod( mean(th(end-1000:end)-phi(end-1000:end)), 2*pi); | |
fprintf('effective period:\t %2.2f\n',Teff) | |
fprintf('rotation number:\t %2.2f\n',Teff/Ten) | |
fprintf('mean phase difference:\t %2.2f\n',phaseDiff) | |
clf | |
subplot(2,1,1) | |
plot(T,[th phi]) | |
subplot(2,1,2) | |
semilogy(T,(abs(th-phi)./T)) | |
%% Compute the map F | |
% F gives the value of theta_n+1 given theta_n. | |
% n correspond to the time t_n : phi(t_n) = 2*n*pi | |
dt = 5e-3; | |
Nt = round( Ten/dt ); | |
N = 200; | |
initialConds = linspace(0,2*pi,N); | |
F = zeros(N,1); | |
th = zeros(Nt,1); | |
for k=1:N | |
th(1) = initialConds(k); | |
for t=1:Nt-1 | |
th(t+1) = th(t) + dt*(m(th(t),dt*t)); | |
end | |
F(k) = th(end); | |
end | |
clf | |
plot(initialConds,F) | |
xlabel('theta n') | |
ylabel('theta n+1') | |
%% Iterate the map F with different initial values | |
Nit = 50; | |
Fs = zeros(Nit,1); | |
clf; hold on | |
for trial=1:20 | |
Fs(1) = 2*pi*rand; | |
for k=2:Nit | |
Fs(k) = interp1( initialConds,F, Fs(k-1) ); | |
Fs(k) = mod(Fs(k),2*pi); | |
end | |
plot(Fs) | |
end | |
%% |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment