Statistical Properties of Neural Networks

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Abstract
Some characteristics of a large population of heterogeneously connected neurons are investigated by a model system composed of McCulloch-Pitts elements. Gross properties are controlled by a few statistical parameters and they show bifurcations. In a synchronous processing algorithm, we find distinct regimes where the system is either monostable, bistable, periodic, or chaotic. In the cyclic processing algorithm which is a kind of asynchronous one, the last two regimes are fussed into a multibasin regime where the system possesses a number of basins of fixed points and chaotic orbits. The number of fixed points is estimated in some regions.