MODELING NEURONS BY SIMPLE MAPS

Abstract

We introduce a simple generalization of graded response formal neurons which presents very complex behavior. Phase diagrams in full parameter space are given, showing regions with fixed points, periodic, quasiperiodic and chaotic behavior. These diagrams also represent the possible time series learnable by the simplest feed-forward network, a two input single-layer perceptron. This simple formal neuron (‘dynamical perceptron’) behaves as an excitable ele ment with characteristics very similar to those appearing in more complicated neuron models like FitzHugh-Nagumo and Hodgkin-Huxley systems: natural threshold for action potentials, dampened subthreshold oscillations, rebound response, repetitive firing under constant input, nerve blocking effect etc. We also introduce an ‘adaptive dynamical perceptron’ as a simple model of a bursting neuron of Rose-Hindmarsh type. We show that networks of such elements are interesting models which lie at the interface of neural networks, coupled map lattices, excitable media and self-organized criticality studies.