A Very Small Chaotic Neural Net

Previously we have shown that chaos can arise in networks of physically realistic neurons (C. Lourenco and A. Babloyantz, 1994), (C. Lourenco, 2006). Those networks contain a moderate to large number of units connected in a spatial arrangement providing instances of so-called cellular neural networks. It was proposed that the flexibility and wide range of behaviors of chaos could be of computational value, namely in spatiotemporal regimes and when coupled with a chaos control process, either in biological or artificial nets. Here we aim to find a minimal network of realistic neurons already featuring a chaotic regime. Such a small network can be computationally useful per se, or otherwise constitute the building block of larger networks with even richer dynamical regimes. Our investigation unveils the role of the interplay between a homoclinic tangency and the presence of delays in neural signal transmission in the creation of complex behavior.