Skip to main content
Figure 1 | The Journal of Mathematical Neuroscience

Figure 1

From: Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

Figure 1

Illustration of the setup in the feedforward network. (A) Two populations connected in a feedforward manner via dynamic synapses. We focus on the connections from neurons j, \(j=1,\ldots ,N\), in the presynaptic population to a specific postsynaptic neuron i. (B) Microscopic picture of N presynaptic spike trains \(s_{j}(t)\) driving the STP dynamics of \(u_{j}(t)\) and \(x_{j}(t)\) for each of the N synapses. The postsynaptic input resulting from synapse j is \(u_{j}(t)x_{j}(t)s_{j}(t)\) and the total postsynaptic input is \(y(t)=N^{-1}\sum_{j=1}^{N}u_{j}(t)x_{j}(t)s_{j}(t)\). (C) Mesoscopic picture of one effective synapse with mean-field STP dynamics driven by the population activity \(A^{N}(t)\) of N neurons. The population activity \(A^{N}(t)\) is defined as the population average of the spike trains of each of the N neurons forming the population. Thus, when the individual spike trains \(s_{j}(t)\) are known, \(A^{N}(t)=N^{-1}\sum_{j=1}^{N} s_{j}(t)\)

Back to article page