High-frequency forced oscillations in neuronlike elements

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2018. Vol. 97. No. 6. P. 062211-1–062211-5.

Zakharov D., Гуткин Б. С., Krupa M., Kuznetsov A.

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.

Keywords: вынужденные колебания, синхронизация, neurons, нейроны, synchronization, Forced oscillations, relaxation oscillator, External force, McKean system, релаксационный осциллятор, внешняя сила

Publication based on the results of: Active and Passive Decoding of the Neural Processes During Cognitive Perfoemance and Neuroeconomic Tasks Execution (2018)