Bonhoeffer-van der Pol oscillator under pulse-train forcing

Avindam Rabinovitch, R. Thieberger, M. Friedman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We analyze the Bonhoeffer-van der Pol equations in a parameter range where no `overt' limit cycle exists, rather the dominating feature in phase space is a focus. Exciting the system by an external pulse, its response depends upon this pulse's size. For small pulses, a quick return to the focus occurs. For large pulses, extending beyond the separatrix, the orbits traverse along a `hidden' structure. This structure initially resembles a temporary limit cycle and then spirals into the focus. The response of the system to single excitations of different sizes at different points of the `hidden' structure is used to understand its response to a train of pulses of different periods. Thus, e.g. the boundaries of the phase- locking regions are easily calculated and the explanation of the appearance of `below threshold' responses for the pulse-train case becomes straightforward.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsWilliam L. Ditto
PublisherPubl by Society of Photo-Optical Instrumentation Engineers
Number of pages5
ISBN (Print)0819412856
StatePublished - 1 Dec 1993
EventChaos in Biology and Medicine - San Diego, CA, USA
Duration: 12 Jul 199313 Jul 1993

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceChaos in Biology and Medicine
CitySan Diego, CA, USA

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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