ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Acebron J. A., Bulsara D., Rappel W. Dynamics оf globally coupled noisy FitzHugh-Nagumo neuron elements. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 3, pp. 110-119. DOI: 10.18500/0869-6632-2003-11-3-110-119

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Language: 
English
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
532.517: 517.9: 621.373
DOI: 
10.18500/0869-6632-2003-11-3-110-119

Dynamics оf globally coupled noisy FitzHugh-Nagumo neuron elements

Autors: 
Acebron J. A., Naval Information Warfare Systems Command (NAVWAR)
Bulsara Dr., Naval Information Warfare Systems Command (NAVWAR)
Rappel W.-J., Naval Information Warfare Systems Command (NAVWAR)
Abstract: 

We study the noisy FitzHugh-Nagumo model in the presence оf аn external sinusoidal driving force. We derive a Fokker-Planck equation for both the single element and for the globally coupled system. We introduce аn 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 оf а stochastic bifurcation.

Key words: 
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Acknowledgments: 
This work has been supported by the Office of Naval Research (Code 331). We also thank the National Partnership for Advanced Computational Infrastructure at the San Diego Supercomputer Center for computing resources.
Reference: 
  1. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 1952;117(4):500-544. DOI: 10.1113/jphysiol.1952.sp004764.
  2. Keener J, Sneyd J. Mathematical Physiology. New York: Springer-Verlag; 1998. 767 p. DOI: 10.1007/b98841.
  3. Longtin А. Effect of noise on the tuning properties of excitable systems. Chaos, Solitons and Fractals. 2000;11(12):1835-1848. DOI: 10.1016/S0960-0779(99)00120-4.
  4. Massanés SR, Pérez Vicente CJ. Classical-like resonance induced by noise in a Fitzhugh–Nagumo neuron model. Int. J. Bifurc. Chaos. 1999;9(12):2295-2303. DOI: 10.1142/S0218127499001784; Massanés SR, Pérez Vicente CJ. Nonadiabatic resonances in a noisy Fitzhugh-Nagumo neuron model. Phys. Rev. E. 1999;59(4):4490-4497. DOI: 10.1103/PhysRevE.59.4490.
  5. Lindner B, Schimansky-Geier L. Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance. Phys. Rev. Е. 1999;60(6):7270-7276. DOI: 10.1103/PhysRevE.60.7270.
  6. Pikovsky AS, Kurths J. Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 1997;78(5):775-778. DOI: 10.1103/PhysRevLett.78.775.
  7. Kurrer С, Schulten K. Noise-induced synchronous neuronal oscillations. Phys. Rev. Е. 1995;51(6):6213-6218. DOI: 10.1103/PhysRevE.51.6213.
  8. Winfree AT. Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media. Chaos. 1991;1(3):303-334. DOI: 10.1063/1.165844.
  9. Hagberg А, Meron Е. Pattern formation in non-gradient reaction-diffusion systems: the effects of front bifurcations. Nonlinearity. 1994;7(3):805. DOI: 10.1088/0951-7715/7/3/006.
  10. Acebrén JA, Bulsara AR, Rappel W-J. submitted for publication.
  11. Risken H. The Fokker-Planck equation: Methods of Solution and Applications. Berlin: Springer Verlag; 1996. 472 p. DOI: 10.1007/978-3-642-61544-3.
  12. Desai RC, Zwanzing R. Statistical mechanics of a nonlinear stochastic model. J. Stat. Phys. 1978;19(1):1-24. DOI: 10.1007/BF01020331.
  13. Shiino M. H-theorem and stability analysis for mean-field models of non-equilibrium phase transitions in stochastic systems. Phys. Lett. A. 1985;112(6-7):302-306. DOI: 10.1016/0375-9601(85)90345-7; Shiino M. Dynamical behavior of stochastic systems of infinitely many coupled nonlinear oscillators exhibiting phase transitions of mean-field type: H theorem on asymptotic approach to equilibrium and critical slowing down of order-parameter fluctuations. Phys. Rev. A. 1987;36(5):2393-2412. DOI: 10.1103/PhysRevA.36.2393.
  14. Tanabe S, Pakdaman K. Dynamics of moments of FitzHugh-Nagumo neuronal models and stochastic bifurcations. Phys. Rev. Е. 2001;63(3):031911. DOI: 10.1103/PhysRevE.63.031911.
Received: 
28.08.2003
Accepted: 
05.10.2003
Available online: 
23.11.2023
Published: 
31.12.2003
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