On the dynamics of analogue neurons with nonsigmoidal gain functions

The characteristic properties of the macroscopic retrieval dynamics of analogue neurons with Hebbian coupling strengths are studied, using the shape of the gain function as a modeling parameter. Already at low loading a rich diversity in dynamical behaviour is observed, covering the full range from point attractors to chaotic dynamics. The attractors which are not of the fixed-point-type, are interpreted as an intermediate phase between the well-known retrieval states and the zero state, enabling a waiting-mode in the system. Using a probabilistic approach it is shown that these features persist in extremely and asymmetrically diluted systems at sufficiently low loading. A number of generic examples are worked out in detail, illustrating some properties of networks governed by nonmonotonic piecewise linear gain functions. The critical storage level above which the chaotic behaviour is absent, is numerically determined.