Abstract
The voltage-controlled oscillator neuromime (VCON) described below is motivated by three things: First, van der Pols equation [1] and similar “flush-and-fill” models have been used since the 1920s to study neural activity. Subsequent work on van der Pols equation resulted in a map of parameter space that describes phase-locking of the oscillator to external forcing [2,3] Second, R. Guttman, et. al., (See 4] used experimental procedures developed by Hodgkin and Huxley for studying squid axon membranes, and they obtained a similar phase-locking portrait for these membranes. This showed that neuron membranes have rich phase-locking, or synchronization properties. Third, I developed and studied a model of a neuron that emphasizes frequency encoded information in [5]. This model is based on a voltage controlled oscillator circuit, and it is called VCON. A VCON provides a straightforward method for building circuit analogs for neural networks, and its associated mathematical model is in phase-amplitude coordinates, so it avoids a major difficulty in dealing with nonlinear oscillators.
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Hoppensteadt, F.C. (1986). Analysis of a VCON Neuromime. In: Othmer, H.G. (eds) Nonlinear Oscillations in Biology and Chemistry. Lecture Notes in Biomathematics, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93318-9_9
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DOI: https://doi.org/10.1007/978-3-642-93318-9_9
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