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High-frequency forced oscillations in neuronlike elements

Abstract : We analyzed a generic relaxation oscillator under moderately strong forcing at a frequency much greater that the natural intrinsic frequency of the oscillator. Additionally, the forcing is of the same sign and, thus, has a nonzero average, matching neuroscience applications. We found that, first, the transition to high-frequency synchronous oscillations occurs mostly through periodic solutions with virtually no chaotic regimes present. Second, the amplitude of the high-frequency oscillations is large, suggesting an important role for these oscillations in applications. Third, the 1:1 synchronized solution may lose stability, and, contrary to other cases, this occurs at smaller, but not at higher frequency differences between intrinsic and forcing oscillations. We analytically built a map that gives an explanation of these properties. Thus, we found a way to substantially “overclock” the oscillator with only a moderately strong external force. Interestingly, in application to neuroscience, both excitatory and inhibitory inputs can force the high-frequency oscillations.
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https://hal.inria.fr/hal-01962910
Contributor : Martin Krupa <>
Submitted on : Thursday, December 20, 2018 - 10:48:45 PM
Last modification on : Monday, October 12, 2020 - 2:28:06 PM

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Denis Zakharov, Martin Krupa, Boris Gutkin, Alexey Kuznetsov. High-frequency forced oscillations in neuronlike elements. Physical Review E , American Physical Society (APS), 2018, 97 (6), ⟨10.1103/PhysRevE.97.062211⟩. ⟨hal-01962910⟩

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