Canards of mixed type in a neural burster

M. Desroches, J. Burke, T. J. Kaper, and M. A. Kramer
Phys. Rev. E 85, 021920 – Published 23 February 2012

Abstract

Canards are solutions of slow-fast systems that spend long times near branches of repelling equilibria, periodic orbits, or higher-dimensional invariant sets. Here, we report on the observation of a new type of canard orbit, labeled a canard of mixed type. This canard orbit is a hybrid of the classical limit cycle canards, which spend long times near attracting and repelling branches of equilibria, and torus canards, which spend long times near attracting and repelling branches of periodic orbits. The canards of mixed type arise in a model of neural bursting activity of fold-fold cycle type, and, as other canard phenomena, separate different dynamic states.

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  • Received 23 September 2011

DOI:https://doi.org/10.1103/PhysRevE.85.021920

©2012 American Physical Society

Authors & Affiliations

M. Desroches1,*, J. Burke2, T. J. Kaper2, and M. A. Kramer2

  • 1Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom
  • 2Department of Mathematics and Statistics, Center for BioDynamics, Boston University, Boston, Massachusetts 02215, USA

  • *INRIA Paris-Rocquencourt Centre, Domaine de Voluceau - BP 105, 78153 Le Chesnay cedex, France.

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Issue

Vol. 85, Iss. 2 — February 2012

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