Browsing by Author "Zakharov, D. G."

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    High-frequency forced oscillations in neuronlike elements
    (APS, 2018-06) Zakharov, D. G.; Krupa, M.; Gutkin, B. S.; Kuznetsov, A. S.; Mechanical and Energy Engineering, School of Engineering and Technology
    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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    On the Dynamical Mechanisms of Influence of Synaptic Currents on the Neuron Model with Response Differentiation
    (Springer, 2015-08) Zakharov, D. G.; Kuznetsov, Alexey S.; Department of Mathematical Sciences, School of Science
    The combined effect of synaptic NMDA, AMPA, and GABA currents on the neuron model with response differentiation has been considered. It has been shown that the GABA and NMDA currents can compensate the effects of each other, whereas the AMPA current not only leads to the suppression of oscillations but also significantly amplifies the high-frequency activity of the neuron induced by the NMDA current. Two bifurcation scenarios underlying these effects have been revealed. It has been predicted which scenario takes place under the combined influence of all three currents.