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What Matters in Neuronal Locking?
Exploiting local stability, we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and, in the limit of a large number of interacting neighbors, also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is adoi:10.1162/neco.19126.96.36.1993 pmid:8888612 fatcat:6jdvmzaejzcd5blmlkxmefbgry