Fig. 1.

Random networks with supralinear dendritic interactions generate transiently increased activity and high-frequency oscillations with frequency 1/τ. (A) A section of the dynamics of a supralinearly coupled network with a synchronous pulse of size g′₀ = 45 generated at time t₀ = 300 ms by external stimulation. This pulse initiates a short-lived chain of propagating, enhanced synchrony. (Bottom) The spiking activity of 200 neurons. Spikes within the chain are marked red. (Middle) The network's spike rate (bin size 1 ms). (Top) The size of synchronous spike pulses within the chain. (B) The propagation of synchrony can be understood quantitatively in Markovian approximation. The chain evolution is characterized by the transition matrix (gray shaded). The dots indicate the mean response pulse sizes derived numerically (green), semianalytically (red), and analytically (blue). Between G₁ and G₂ a range with high probability of amplification exists. The gray dashed line shows the evolution of the event in A. (Inset) The dendritic modulation function σ (black line) mapping the peak excitatory postsynaptic potential (EPSP) expected from linear input summation to the effective peak EPSP.