Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle

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Abstract

We present two hypotheses on the mathematical mechanism underlying bursting dynamics in a class of differential systems: (1) that the transition from continuous firing of spikes to bursting is caused by a crisis which destabilizes a chaotic state of continuous spiking; and (2) that the bursting corresponds to a homoclinicity to this unstable chaotic state. These propositions are supported by a numerical test on the Hindmarsh-Rose model, a prototype of its kind. We conclude by a unified view for three types of complex multi-modal oscillations: homoclinic systems, bursting, and the Pomeau-Manneville intermittency.

Original languageEnglish (US)
Pages (from-to)263-274
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Volume62
Issue number1-4
DOIs
StatePublished - Jan 30 1993

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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