Coupled Neuronal Oscillatory Systems

  • Julie Hyde
Conference paper
Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)


Central pattern generators can be modelled by systems of coupled oscillators. A technique of applying spatio-temporal symmetries to such models is discussed as a possible approach to classifying respiratory patternings in vertebrates.


Dopamine Respiration Hyde 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Selverston AI. Are central pattern generators understandable? The behavioural and brain sciences. 1980; 3:535–571CrossRefGoogle Scholar
  2. [2]
    Winlow W, Moroz LL & Syed NI. Chapter 4, Mechanisms of behavioural selection in Lymnaea stagnalis. To be published.Google Scholar
  3. [3]
    Syed NI, Bulloch AGM & Lukowiak K. In vitro reconstruction of the respiratory central pattern generator of the mollusc Lymnaea. Science reports 1990; 250:282–285Google Scholar
  4. [4]
    Kuramoto Y. Synchronisation of pulse-coupled oscillators and excitable units. Physica D May 1991; 50:15–30MATHGoogle Scholar
  5. [5]
    Biktashev VM & Molchanov AM. Macrodynamical approach to the analysis of neural networks. Research Computing Center, Puschino. 142292, USSR. Preprint.Google Scholar
  6. [6]
    Holden AV. The mathematics of excitation. In: Ricciardi LM & Scott A (eds) Biomathematics in 1980. North-Holland Amsterdam, 1982Google Scholar
  7. [7]
    Petersen CK. Techniques to trace curves of bifurcation points of periodic solutions. Path User’s Guide. Centre for nonlinear studies, Leeds, 1987Google Scholar
  8. [8]
    Doedel EJ. AUTO-Software for continuation and bifurcation problems in ordinary differential equations. Calif Inst Tech, 1986Google Scholar
  9. [9]
    Barbi M, Haydon PG, Holden AV& Winlow W. On the phase response curves of repetitively active neurones. J Theor Neurobiol 1984; 3:15–24Google Scholar
  10. [10]
    Hyde J & Rubio JE. Synthesis of isochrones. In preparation.Google Scholar
  11. [11]
    Baesens C, Guckenheimer J, Kim S & MacKay RS. Three coupled oscillators: mode locking, global bifurcations and toroidal chaos. Physica D no 3, 1991; 49:387–475CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    Rubio JE. A new mathematical model of the respiratory centers. Bull math biophys 1972; 34:467–481CrossRefGoogle Scholar
  13. [13]
    Golubitsky M, Stewart I & Schaeffer DG. Singularities and groups in bifurcation theory. Appl math sci 69, vol 2. Springer, Berlin Heidelberg New York, 1988CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1992

Authors and Affiliations

  • Julie Hyde
    • 1
  1. 1.Depts. of Applied Mathematical Studies and PhysiologyUniversity of LeedsLeedsUK

Personalised recommendations