//// Simulation of (leaky) integrate-and-fire neuron
 clear; clf;

//// parameters of the model
 dt=0.1;       // integration time step [ms]
 tau=10;       // time constant [ms]
 E_L=-65;      // resting potential [mV]
 theta=-55;    // firing threshold [mV]
 RI_ext=12;     // constant external input [mA/Ohm]
 
//// Integration with Euler method
 t_step=0; v=E_L;
 for t=0:dt:100;
     t_step=t_step+1;
     s=v>theta;
     v=s*E_L+(1-s)*(v-dt/tau*((v-E_L)-RI_ext));
     v_rec(t_step)=v;
     t_rec(t_step)=t;
     s_rec(t_step)=s;
 end

//// Plotting results
   plot(t_rec,v_rec);
   plot([0 100],[-55 -55],'--');
   xlabel('Time [ms]'); ylabel('v [mV]')