Figure 2. .

The formation of interconnected memory representations in a plastic neural network. (A) In a recurrent network 𝒩, two neuronal populations (1: black; 2: yellow) receive specific external inputs of average amplitudes ${\tilde{F}}_1^{\text{ex}}$ and ${\tilde{F}}_2^{\text{ex}}$. All remaining neurons of the network (blue) are combined to a background population ℬ and serve as control neurons receiving noisy external inputs. Each population p ∈{1, 2, ℬ} is described by its mean intra-population-synaptic weight ${\tilde{\omega }}_{pp}$, its mean activity ${\tilde{F}}_p$, and its connections to other populations (p′∈{1, 2, ℬ}∖p) via a set of synapses with average synaptic strength ${\tilde{\omega }}_{p^{\prime }p}$. (B) The abstraction of the neuronal network model yields a low-dimensional one described by the mean equilibrium activities (𝔉) and corresponding mean equilibrium synaptic weights (𝔴_p′p). Here, the external input (red) combines inputs from background neurons and external inputs given in the complete network model (A). (C) In the network model (A), changing the amplitude of the external input to neuronal populations 1 (black) and 2 (yellow) at t = 10 yields increased average activities within the populations and background neurons (blue), triggering synaptic changes. Gray lines indicate single neuron/synapse dynamics. After a brief period, all system variables reach an equilibrium state. This state is matched very well by the theoretical analysis (green lines) considering the abstract model (B). (i) Inputs; (ii) average activities of each population; (iii) average intrapopulation synaptic weights; (iv) average interpopulation synaptic weights. The average input amplitudes are determined by two Ornstein-Uhlenbeck processes with mean ${\tilde{F}}_1^{\text{ex}}=0.9$ and ${\tilde{F}}_2^{\text{ex}}=0.75$.