Simple models for excitable and oscillatory neural networks |
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Authors: | David Taylor Philip Holmes |
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Institution: | (1) Iomega Corporation, 800 Tasman Drive, Milpitas, CA 95035, USA, US;(2) Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544-5263, USA, US |
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Abstract: | Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion
in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with
brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting
dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications
thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave
patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators
providing input to a kinematic musculature model of lamprey..
Received: 25 November 1996 / Revised version: 9 December 1997 |
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Keywords: | : Bifurcation Coupling Oscillator Network |
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