High-frequency forced oscillations in neuronlike elements

Denis Zakharov (1) , Martin Krupa (2, 3, 4) , Boris Gutkin (5) , Alexey Kuznetsov (6)

1 Institute of Applied Physics of RAS
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
4 MATHNEURO - Mathématiques pour les Neurosciences
5 ENS-PSL - École normale supérieure - Paris
6 IUPUI - Indiana University - Purdue University Indianapolis

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.

Domaines: Systèmes dynamiques [math.DS]

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