Spike-Generating Dynamical Systems and Networks

The word “spike” is a term for nerve cell electrical discharges. The description of a spike may be detailed or be restricted to the existence of a neural happening. Thus Hodgkin and Huxley (1952) described spikes by a nonlinear PDE coupled with 3 ODEs. However, McCulloch and Pitts (1943) applied logical constants which might also represent spikes. The choice of model strongly influences the speed of simulations and the tractability of problems. This paper suggests that both approaches may contribute to our knowledge. Moreover, present tools permit the design of intermediary models that are amenable to analysis — since generated by short algorithms — and which at the same time display complicated behaviors (May, 1976). Autonomous piecewise linear maps may be universal in generating interspike patterns or strange “neural” discharges (Labos, 1981; Nogradi and Labos, 1981). Two such systems, called polynomial spike generator (PSG) and universal pattern generator (UPG) will be discussed besides formal neural nets (FNNs).