SpringerLink
Log in

Pulse-Coupled Oscillators

  • Reference work entry
  • First Online:
Encyclopedia of Computational Neuroscience

  • 48 Accesses

Definition

Pulse-coupled oscillators are intrinsically rhythmic circuit elements (oscillators) that are coupled via instantaneous interactions. Pulse (or pulsatile) coupling is only approximate because real world pulses cannot exert their effects instantaneously. Instead, a finite amount of time must elapse in order to produce an effect. However, the theoretical results for pulse-coupled oscillators generally apply to cases in which the input pulse exerts its effects during a time window of finite duration, provided that this duration is short compared to the period of the oscillation.

Detailed Description

This article focuses on neural oscillators, or intrinsically rhythmic nerve cells (neurons). Neurons are well suited to an analysis based on pulse coupling because they communicate via action potentials, also called spikes, which are all or nothing electrical signals that trigger a cascade of events leading to a somewhat slower, graded response in the target neuron. Coherent...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Buzsaki G (2006) Rhythms of the brain. Oxford University Press, Oxford

    Book  Google Scholar 

  • Canavier CC (2005) Analysis of circuits containing bursting neurons using phase resetting curves. In: Coombes S, Bressloff P (eds) Bursting: the genesis of rhythm in the nervous system. World Scientific, Singapore, pp 175–200

    Chapter  Google Scholar 

  • Canavier CC, Achuthan SA (2010) Pulse coupled oscillators and the phase resetting curve. Math Biosci 226:77–96

    Article  PubMed  PubMed Central  Google Scholar 

  • Canavier CC, Achuthan SA (2012) History of the application of the phase resetting curve to neurons coupled in a pulsatile manner. In: Schultheiss NW, Prinz AA, Butera RJ (eds) Phase response curves in neuroscience: theory, experiment and analysis. Springer, New York, pp 73–94

    Chapter  Google Scholar 

  • Ermentrout GB, Chow CC (2002) Modeling neural oscillations. Physiol Behav 77:629–633

    Article  CAS  PubMed  Google Scholar 

  • Ermentrout GB, Terman DH (2010) Mathematical foundations of neuroscience. Springer, New York, pp 193–194

    Book  Google Scholar 

  • Glass L, Mackey MC (1988) From clocks to chaos. Princeton University Press, Princeton

    Book  Google Scholar 

  • Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, New York

    Book  Google Scholar 

  • Izhikevich EM (2007) Dynamical systems in neuroscience: the geometry of excitability and bursting. The MIT Press, Cambridge, MA. Chapter 10. http://www.izhikevich.com

    Google Scholar 

  • Pikovsky A, Rosenblum M, Kurths J (2001) Synchronization: a universal concept in nonlinear sciences. Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  • Rinzel J, Ermentrout B (1998) Analysis of neural excitability and oscillations. In: Koch C, Segev I (eds) Methods in neuronal modeling: from ions to networks. The MIT Press, Cambridge, MA, pp 251–292

    Google Scholar 

  • Schultheiss NW, Prinz AA, Butera RJ (eds) (2012) Phase response curves in neuroscience: theory, experiment and analysis. Springer, New York, p 73

    Book  Google Scholar 

  • Wang X-J (2010) Neurophysiological and computational principles of cortical rhythms in cognition. Physiol Rev 90:1195–1268

    Article  PubMed  Google Scholar 

  • Wiggins S (1990) Introduction to applied nonlinear dynamical systems and chaos. Springer, New York

    Book  Google Scholar 

  • Winfree A (2001) The geometry of biological time. Springer, Berlin

    Book  Google Scholar 

Further Reading

  • Achuthan S, Canavier CC (2009) Phase resetting curves determine synchronization, phase-locking, and clustering in networks of neural oscillators. J Neurosci 29(16):5218–5233

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Goel P, Ermentrout B (2002) Synchrony, stability, and firing patterns in pulse-coupled oscillators. Physica D 163(191–216):2002

    Google Scholar 

  • Mirollo RE, Strogatz SH (1990) Synchronization of pulse-coupled biological oscillators. SIAM J Appl Math 50:1645–1662

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Cell Biology and Anatomy, LSU Health Sciences Center, New Orleans, LA, USA

    Carmen C. Canavier

Authors
  1. Carmen C. Canavier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carmen C. Canavier .

Editor information

Editors and Affiliations

  1. Emory University, Atlanta, GA, USA

    Dieter Jaeger

  2. University of Arkansas, Fayetteville, AR, USA

    Ranu Jung

Section Editor information

  1. National Research Council, Institute of Biophysics, Palermo, Italy

    Michele Migliore

  2. Computational Physiology Lab, Department of Neurobiology and Behavior, Cornell University, Ithaca, NY, USA

    Christiane Linster

  3. Department of Biology, Emory University, Atlanta, GA, USA

    Francesco Cavarretta

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Science+Business Media, LLC, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Canavier, C.C. (2022). Pulse-Coupled Oscillators. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-1006-0_269

Download citation

Publish with us

Policies and ethics

Search

Navigation