Oscillatory States in Coupled Neural Oscillators

Abstract

Two different kinds of analogous model neurons have been investigated so far, namely, the Hop-field type neuron characterized by a sigmoid function, and Hoppensteadt’s voltage controlled oscillator (VCO). Both neurons can be implemented by means of electronic circuits composed of operational amplifiers and linear elements. Whereas Hopfield nets have been mainly applied to cognitive tasks such as content addressable memory, and more recently also to the storage of cycles of states, VCO neurons are used to simulate endogenous bursting neurons (EBN), i. e., they produce bursts of output peaks with a constant frequency. In order to provide a link between Hopfield and VCO neurons we construct a nonlinear oscillator by coupling a pair of Hopfield neurons asymmetrically. This oscillator can be regarded as one EBN as it is mimiced by a VCO, where its square wave output is interpreted as the envelope of an EBN’s burst. We have implemented a network of four cyclically coupled oscillators (eight neurons) electronically and compared the observed wave forms with those predicted by the Hopf bifurcation theory with symmetry. The experiments show that all generic oscillatory states of the theory can occur in the network.