High-frequency forced oscillations in neuronlike elements.

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.

[A two-compartment phenomenological model of a dopaminergic neuron].

A two-compartment model of the dopaminergic neuron based on modified FitzHue-Nagumo oscillators for each compartment has been built. The compartments corresponded to the soma and dendrites and differed by the values of small parameters. The influence of stimuli (applied current for the somatic compartment and synaptic activation for the dendritic compartment) on the model has been studied. It has been shown that the activation of AMPA and NMDA synaptic currents lead to the generation of high-frequency bursts by the neuron. The mechanisms underlying the generation of the bursts have been investigated.

[Synchronization in a model of interacting inferior olive cells with variable electrotonic coupling].

Synchronization processes have been studied within the framework of a model describing the dynamics of two inferior olive cells coupled electrotonically through gap junctions surrounded by synaptic inhibitory terminals that block these couplings. A simple model of a chemical synaptic terminal based on the first-order kinetics has been constructed to describe the coupling break. It was found that different types of synchronous behavior exist in the system, depending on the parameters. These are 1:1 and 1:2 synchronization regimes, spike time binding, and others. It was demonstrated that even small changes in the coupling parameters (coupling strength and coupling break delay) may significantly affect the synchronous regimes of interacting cells. In some cases, the activity of one of inferior olive cells is suppressed due to collective dynamics, whereas the activity of the other cell is conserved.