DOI 10.1007/s11063-005-0667-6 Neural Processing Letters (2005) 22:57–68 © Springer 2005 Refractoriness in Poisson and Gaussian First-order Neural Nets with Chemical Markers ELENI FOURNOU 1 , PANOS ARGYRAKIS 2,⋆ and PHOTIOS A. ANNINOS 3 1 Department of Applied Sciences, Technological Education Institution (TEI) of Thessaloniki, 57400 Sindos, Greece. e-mail: efournou@gen.teithe.gr 2 Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece. e-mail: panos@physics.auth.gr 3 Department of Medical Physics, University of Thraki, 68100 Alexandroupolis, Greece. e-mail: anninos@axd.forthnet.gr Abstract. In this work first order probabilistic Poisson and Gaussian neural nets with chem- ical markers are investigated, analytically and by computer simulations. The investigation of steady-state behavior of these systems is extended here to systems in which the refrac- tory period is assigned to be 1 for all or some of the subpopulations of the net, whereas the remainder are characterized by zero refractory periods. The interest is focused on the effects of refractoriness on the neural activities. Results obtained show the existence of sev- eral critical points at high initial activities, which are a consequence of the nonzero refrac- tory periods. For these points a larger initial activity, above a certain critical level, results in the reduction of activity to a lower stable steady-state, instead of the highest one. We also find that in the Gaussian nets each critical point is lower than the corresponding one as in the Poisson nets. Finally, a discussion of the results is made. Key words. chemical markers, neural nets, refractoriness 1. Introduction An area of considerable importance is that of biological nets, i.e. models of nets that try to imitate the human or other living brain structure and functions in an effort to understand such vital processes as memory, learning, understanding, etc. Widely used models (not an exhaustive list) include the early pioneer work of McCulloch and Pitts of assemblies of neurons as logical decision elements [1], the mathematical formalism of Caianiello of the ‘neuronic equation’ [2], and the prob- abilistic neural structure [3–6] that monitor the neural activity, i.e. the fraction of neurons that become active per unit time. These models have been quite success- ful towards our understanding of the above mentioned functions. In these models a network is made of a large number of neurons (the elementary unit), which are interconnected according to some rules. As each unit has several connections, and there is a large number of units, it is quickly realized that the number of connec- tions grows very fast, making the task of calculations quite difficult. But it should ⋆ Corresponding author.