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We have examined the problem of obtaining relationships between the type of stable solutions of the Hodgkin-Huxley type system, the values of its parameters and a constant applied current (I). As variable parameters of the system the maximal Na+(-gNa), K+(-gK) conductances and shifts (Gm, Gh, Gn) of the voltage-dependences have been chosen. To solve this problem it is sufficient to find points belonging to the boundary, partitioning the parameter space of the system into the regions of the qualitatively different types of stable solutions (steady states and stable periodic oscillations). Almost all over the physiological range of I, a type of stable solution is determined by the type of steady state (stable or unstable). Using this fact, the approximate solution of this problem could be obtained by analyzing the spectrum of eigenvalues of the Jacobian matrix for the linearized system. The families of the plan sections of the boundary have been constructed in the three-parameter spaces (I, -gNa, -gK), (I, Gm, Gh), (I, Gm, Gn).

The task of estimating the functional state of the CNS with the pain syndrome in patients with anxious phobic disorders is examined. For solving the task, the methods of spectral and multifractal analyses of EEG segments are applied during the perception of psychogenic pain and its removal by the psychorelax ation technique. It has been demonstrated that contrary to power spectra, singularity spectra allow distin guishing EEGs quantitatively in the examined functional states of the brain. Pain suppression in patients with anxious phobic disorders during psychorelaxation is accompanied by changing the width of the singularity spectrum and approximation of the multifractal parameter to the value corresponding to healthy subjects.

The use of the mathematical model of rat nociceptive neuron membrane allowed us to predict a new mechanism of suppression of ectopic bursting discharges, which arise in neurons of dorsal root ganglia and are one of the causes of neuropathic pain. The treatment with comenic acid leads to switching off the ectopic bursting discharges due to a decrease in the effective charge transferring via the activation gating structure of the slow sodium channels (Na 1.8a). Comenic acid is a drug substance of a new non-opioid analgesic [1] Thus, this analgesic not only reduces the frequency of rhythmic discharges of nociceptive neuron membrane [2] but also it suppresses its ectopic bursting discharges.

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