Journal of Mathematical Biology

, Volume 37, Issue 5, pp 419–446 | Cite as

Simple models for excitable and oscillatory neural networks

  • David Taylor
  • Philip Holmes

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..

Key words: Bifurcation Coupling Oscillator Network 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • David Taylor
    • 1
  • Philip Holmes
    • 2
  1. 1.Iomega Corporation, 800 Tasman Drive, Milpitas, CA 95035, USAUS
  2. 2.Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544-5263, USAUS

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