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The qualitative behavior of the differential equation, where  x  is real and  f  is periodic in  t , is determined by the attracting periodic solutions. This article gives an exposition of a method of Ilyashenko that uses complex analysis to determine an upper bound on the number of periodic solutions. The method is then applied to a well-known model of a single neuron or pool of neurons.

Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model