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Dynamics of Globally Coupled Noisy Excitable Elements: The Fitzhugh-Nagumo Case

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IUTAM Symposium on Nonlinear Stochastic Dynamics

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 110))

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Abstract

We study the noisy FitzHugh-Nagumo model in the presence of an external sinusoidal driving force. We derive a Fokker-Planck equation for both the single element and for the globally coupled system. We introduce an efficient way to numerically solve this Fokker-Planck equation and show that the external driving force leads to a classical resonance when its frequency matches the underlying systems frequency. This resonance is also investigated analytically by exploiting the different timescales in the problem. Agreement between the analytical results and numerical results is excellent and reveals the existence of a stochastic bifurcation.

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Author information

Authors and Affiliations

  1. Department of Physics, University of California, San Diego, La Jolla, CA, 92093, USA

    J. A. Acebrón & W.-J. Rappel

  2. SPAWAR Systems Center Code D363, 49590 Lassing Road, RM A341, San Diego, CA, 92152-6147

    A. R. Bulsara

Authors
  1. J. A. Acebrón
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  2. A. R. Bulsara
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  3. W.-J. Rappel
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Editor information

Editors and Affiliations

  1. University of Illinois at Urbana-Champaign, USA

    N. Sri Namachchivaya

  2. Florida Atlantic University, USA

    Y. K. Lin

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© 2003 Springer Science+Business Media Dordrecht

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Acebrón, J.A., Bulsara, A.R., Rappel, WJ. (2003). Dynamics of Globally Coupled Noisy Excitable Elements: The Fitzhugh-Nagumo Case. In: Namachchivaya, N.S., Lin, Y.K. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics. Solid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0179-3_9

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  • DOI: https://doi.org/10.1007/978-94-010-0179-3_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3985-7

  • Online ISBN: 978-94-010-0179-3

  • eBook Packages: Springer Book Archive

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