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Delay-Induced Multistability in a Generic Model for Excitable Dynamics

[+] Author Affiliations
Johanne Hizanidis, Roland Aust, Eckehard Schöll

Technical University of Berlin, Berlin, Germany

Paper No. DETC2007-34329, pp. 687-694; 8 pages
doi:10.1115/DETC2007-34329
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

Motivated by real-world excitable systems such as neuron models and lasers, we consider a paradigmatic model for excitability with a global bifurcation, namely a saddle-node bifurcation on a limit cycle. We study the effect of a time-delayed feedback force in the form of the difference between a system variable at a certain time and at a delayed time. In the absence of delay the only attractor in the system in the excitability regime, below the global bifurcation, is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling as well as saddle-node bifurcations of limit cycles are found in accordance with Shilnikov’s theorems.

Copyright © 2007 by ASME

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