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Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062916. Epub 2014 Jun 17.

Theoretical analysis of vibrational resonance in a neuron model near a bifurcation point.

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School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People's Republic of China.
School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222, People's Republic of China.


The FitzHugh-Nagumo neuron model subject to a biharmonical external force with two different frequencies is used to investigate the underlying mechanism of vibrational resonance in an excitable system in which the time scales between the fast and slow variables are separated clearly. The theoretical analysis is given based on the approximation approach and the concept of the phase-locking ratio instead of the amplification ratio widely used in the investigation of vibrational resonance in bistable oscillators. The result shows that the high-frequency subthreshold force with the frequency close to the natural frequency of the neuron model in the resting state can induce the change of potential shape of the model near the bifurcation point. This gives rise to the different phase-locking modes of the neuron responses to the same low-frequency subthreshold input. It is also shown that besides the parameters of the high-frequency force such as amplitude and frequency, the bifurcation parameter of the model can affect the vibrational resonance notably. Finally, the numerical results have verified the theoretical analysis.

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