Fig. 7

Antisymmetric STDP learning for a network of $n=3$ neurons. (a) Temporal evolution of the inputs to the network. The three neurons are successively and periodically excited. The red color corresponds to an excitation of 1 and the blue to no excitation. (b) Equilibrium connectivity. The matrix is antisymmetric and shows that neurons excite one of their neighbors and are inhibited by the other. (c) Temporal evolution of the connectivity strength. The colors correspond to those of (b). The connectivity of system (17) corresponds to the plain thin oscillatory curves. The connectivity of the averaged system (18) (with $k,q<4$) corresponds to the plain thick lines. Note that each curve corresponds to the superposition of three connections which remain equal through learning. The dashed curves correspond to the antisymmetric part in (19). The parameters chosen for this simulation were $l=10$, $\kappa =100$, $\gamma =3$, $a_{+}=a_{-}=1$, $\tau =3$, $\sigma =0.001$, $\mu =1$, $ϵ=0.001$. The system was simulated on the fast time-scale during $T=10\text{,}000$ time steps of size $dt=0.01$.