The population activity in a homogeneous pool of spiking neurons can be described by an integral equation (similar to the original Wilson-Cowan model) which is exact in the limit of N \rightarrow . Typical dynamical states may be analyzed directly on the level of the integral equation.

(i) fast transients: populations of spiking neurons react instanteneously to step changes in the input (it cf. Tsodyks and Sejnowski; Van Vreewsijk and Sompolinsky) --- which shows that a description of the population activity A with a standard first-order differential equation is not valid (at least not during the initial phase of the transient).

(ii) The `locking' condition that we have studied earlier, (paper with van Hemmen and Cowan) has a natural generalization in the context of the integral equation.

(iii) Stability of incoherent firing states (splay phase) may be analyzed in the presence of noise as a function of parameters like the transmission delay.

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