Figure 1.

Adaptive nodes in a feedforward network. (a) A schema of N input units connected with fixed weights (synapses), W_m, to K terminals (dendrites) which are connected with adaptive weights, J_i, to an output unit. Delays between input units and the output unit are denoted by τ_m and the dynamics of the output unit is governed by leaky integrated-and-fire neuron, eq. (1). After an adaptation step, $J_i^{+}$ is a function of its relative change, δ, and an additive noise, η, eq. (2). (b) A typical profile of δ = 0.05 * exp(−|Δ|/15) * sign(Δ) (solid blue line), where Δ measures the time-lag between a sub-threshold stimulation arriving from a terminal and another one which generates a spike. Δ is measured in ms. A simplified two-level adaptive rule (dashed blue line). Both adaptive rules have a cutoff at 50 ms. (c) Simulation results of (a) with K = 3 and N = 15, where inputs are stimulated simultaneously at 5 Hz. Three types of stationary solutions for J_i were found: (c₁) Fixed values. (c₂) Fast oscillations characterized by relatively small fluctuations around a fixed value. (c₃) Slow oscillations characterized by large fluctuations and semi-flat periods at extreme values. (d) Fraction of the three types of stationary solutions in (c), as a function of N/K for K = 3, obtained in exhaustive search simulations (Methods). (e) Number of different stationary firing patterns, attractors, and their standard deviation, for K = 3 and N = 9 as a function of the number of different random initial conditions for W_m (Methods).