Abstract
Self-organization of frequencies is studied by using model neurons called VCONs (voltage-controlled oscillator neuron models). These models give direct access to frequency information, in contrast to all-or-none neuron models, and they generate voltage spikes that phase-lock to oscillatory stimulation, similar to phase-locking of action potentials to oscillatory voltage stimulation observed in Hodgkin-Huxley preparations of squid axons. The rotation vector method is described and used to study how networks synchronize, even in the presence of noise or when damaged; the entropy of ratios of phases is used to construct an energy function that characterizes organized behavior. Computer simulations show that rotation numbers (output frequency/input frequency) describe both chaotic and nonchaotic behavior. Learning occurs when synaptic connections strengthen in response to stimulation that is synchronous with cell activity. It is shown that intermittent chaotic firing is suppressed and simple stable responses are enhanced by such learning in VCON networks. This analysis provides a rigorous basis for further investigation of the ideas of Wiener [Wiener, N. (1961) Cybernetics (MIT Press, Cambridge, MA), p. 191] on the origin of slow brain waves due to "the pulling together of frequencies."