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

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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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532.517: 517.9: 621.373

Dynamics оf globally coupled noisy FitzHugh-Nagumo neuron elements

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)

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.

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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.
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