Mixed-mode oscillations

from neural phenomena to mechanical modelling

I. Kovacic, M. Zukovic, M.P. Cartmell

Research output: Contribution to conferenceOther

Abstract

This paper offers new results from a study of mixed-mode oscillations, with application to both neural and mechanical systems. It is initially shown that the Fitzhugh-Nagumo model, which is itself a simplification of the previous electrophysiological model of Hodgkin and Huxley, has a direct analogue in the form of the model for a bistable spring mass system. This system is then shown to exhibit three qualitatively different motions and the design parameter space for the oscillator is examined in order to define conditions for these and for mixed-mode oscillations. The paper concludes with a conjecture that an autonomous system of this form can display some of the dynamic characteristics of the autonomous van der Pol oscillator, and one example of this equivalence is examined numerically.
Original languageEnglish
Number of pages6
DOIs
Publication statusPublished - 2015

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Direct analogs

Keywords

  • oscillators
  • mathematical model
  • force
  • trajectory
  • integrated circuit modeling
  • springs
  • Fitzhugh-Nagumo model

Cite this

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title = "Mixed-mode oscillations: from neural phenomena to mechanical modelling",
abstract = "This paper offers new results from a study of mixed-mode oscillations, with application to both neural and mechanical systems. It is initially shown that the Fitzhugh-Nagumo model, which is itself a simplification of the previous electrophysiological model of Hodgkin and Huxley, has a direct analogue in the form of the model for a bistable spring mass system. This system is then shown to exhibit three qualitatively different motions and the design parameter space for the oscillator is examined in order to define conditions for these and for mixed-mode oscillations. The paper concludes with a conjecture that an autonomous system of this form can display some of the dynamic characteristics of the autonomous van der Pol oscillator, and one example of this equivalence is examined numerically.",
keywords = "oscillators, mathematical model, force, trajectory, integrated circuit modeling, springs, Fitzhugh-Nagumo model",
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Mixed-mode oscillations : from neural phenomena to mechanical modelling. / Kovacic, I.; Zukovic, M.; Cartmell, M.P.

2015.

Research output: Contribution to conferenceOther

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T2 - from neural phenomena to mechanical modelling

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AU - Zukovic, M.

AU - Cartmell, M.P.

PY - 2015

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N2 - This paper offers new results from a study of mixed-mode oscillations, with application to both neural and mechanical systems. It is initially shown that the Fitzhugh-Nagumo model, which is itself a simplification of the previous electrophysiological model of Hodgkin and Huxley, has a direct analogue in the form of the model for a bistable spring mass system. This system is then shown to exhibit three qualitatively different motions and the design parameter space for the oscillator is examined in order to define conditions for these and for mixed-mode oscillations. The paper concludes with a conjecture that an autonomous system of this form can display some of the dynamic characteristics of the autonomous van der Pol oscillator, and one example of this equivalence is examined numerically.

AB - This paper offers new results from a study of mixed-mode oscillations, with application to both neural and mechanical systems. It is initially shown that the Fitzhugh-Nagumo model, which is itself a simplification of the previous electrophysiological model of Hodgkin and Huxley, has a direct analogue in the form of the model for a bistable spring mass system. This system is then shown to exhibit three qualitatively different motions and the design parameter space for the oscillator is examined in order to define conditions for these and for mixed-mode oscillations. The paper concludes with a conjecture that an autonomous system of this form can display some of the dynamic characteristics of the autonomous van der Pol oscillator, and one example of this equivalence is examined numerically.

KW - oscillators

KW - mathematical model

KW - force

KW - trajectory

KW - integrated circuit modeling

KW - springs

KW - Fitzhugh-Nagumo model

U2 - 10.1109/BIBE.2015.7367631

DO - 10.1109/BIBE.2015.7367631

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ER -