Oscillations via Spike-Timing Dependent Plasticity in a Feed-Forward Model
Fig 5
Numerical simulations of the STDP-driven synaptic dynamics of 1200 excitatory synapses in an isotropic “Ring Model” architecture, serving as feed-forward input onto a single conductance based post-synaptic neuron (see Methods for details).
The pre-synaptic activity followed eq (17), with N = 1200, D = 10Sp/sec, A = 10Sp/sec and a varying angular frequency ν. Here we simulated the temporally anti-symmetric exponential STDP rule (eq (4) with τ± = 20ms), with α = 1, μ = 0, using a learning rate constant λ = 5·10−3. (A) The angular velocity V of the order parameter ψ (eq (34) in Revolutions per Hour—RPH) is plotted as a function of the oscillation frequency. (B, C and D) The synaptic weight profile as estimated numerically (calculated from the second half of the simulations, following convergence to the limit cycle), shown as a function of the pre-post phase difference, in red. Note the weight profile and the post phase drift at the same velocity, in red. The black curve shows the zero drift solution of eq (40). The vertical dashed gray line depicts the order parameter or “center of mass” ψ0 of the zero drift solution, the dashed blue line shows ψ0 + νd, and the pink line shows the “center of mass” ψ of the weight profile of the limit cycle solution. The panels differ in terms of the oscillation frequency of the pre-synaptic population and 36 Hz for panels B, C, and D, respectively.