% spnet.m: Spiking network with axonal conduction delays and STDP
% Created by Eugene M.Izhikevich.                February 3, 2004
M=100;                 % number of synapses per neuron
D=20;                  % maximal conduction delay 
% excitatory neurons   % inhibitory neurons      % total number 
Ne=800;                Ni=200;                   N=Ne+Ni;
a=[0.02*ones(Ne,1);    0.1*ones(Ni,1)];
d=[   8*ones(Ne,1);    2*ones(Ni,1)];
sm=10;                 % maximal synaptic strength

post=ceil([N*rand(Ne,M);Ne*rand(Ni,M)]); 
s=[6*ones(Ne,M);-5*ones(Ni,M)];         % synaptic weights
sd=zeros(N,M);                          % their derivatives
for i=1:N
  if i<=Ne
    for j=1:D
      delays{i,j}=M/D*(j-1)+(1:M/D);
    end;
  else
    delays{i,1}=1:M;
  end;
  pre{i}=find(post==i&s>0);             % pre excitatory neurons
  aux{i}=N*(D-1-ceil(ceil(pre{i}/N)/(M/D)))+1+mod(pre{i}-1,N);
end;
STDP = zeros(N,1001+D);
v = -65*ones(N,1);                      % initial values
u = 0.2.*v;                             % initial values
firings=[-D 0];                         % spike timings

for sec=1:60*60*24                      % simulation of 1 day
  for t=1:1000                          % simulation of 1 sec
    I=zeros(N,1);        
    I(ceil(N*rand))=20;                 % random thalamic input 
    fired = find(v>=30);                % indices of fired neurons
    v(fired)=-65;  
    u(fired)=u(fired)+d(fired);
    STDP(fired,t+D)=0.1;
    for k=1:length(fired)
      sd(pre{fired(k)})=sd(pre{fired(k)})+STDP(N*t+aux{fired(k)});
    end;
    firings=[firings;t*ones(length(fired),1),fired];
    k=size(firings,1);
    while firings(k,1)>t-D
      del=delays{firings(k,2),t-firings(k,1)+1};
      ind = post(firings(k,2),del);
      I(ind)=I(ind)+s(firings(k,2), del)';
      sd(firings(k,2),del)=sd(firings(k,2),del)-1.2*STDP(ind,t+D)';
      k=k-1;
    end;
    v=v+0.5*((0.04*v+5).*v+140-u+I);    % for numerical 
    v=v+0.5*((0.04*v+5).*v+140-u+I);    % stability time 
    u=u+a.*(0.2*v-u);                   % step is 0.5 ms
    STDP(:,t+D+1)=0.95*STDP(:,t+D);     % tau = 20 ms
  end;
  plot(firings(:,1),firings(:,2),'.');
  axis([0 1000 0 N]); drawnow;
  STDP(:,1:D+1)=STDP(:,1001:1001+D);
  ind = find(firings(:,1) > 1001-D);
  firings=[-D 0;firings(ind,1)-1000,firings(ind,2)];
  s(1:Ne,:)=max(0,min(sm,0.01+s(1:Ne,:)+sd(1:Ne,:)));
  sd=0.9*sd;
end;