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In this paper we consider the Brusselator and the Sel'kov model, which describes the irreversible reaction of glycolysis in the regime of self-sustained oscillations. We show that these two differently constructed models can be reduced to a single equation -- a generalized Rayleigh equation. The physical basis for this generality is investigated. The advantages of this equation as a tool for qualitative and quantitative analyses, as well as the similarities and differences of the solutions realized for each of the two concrete models in the cases of almost harmonic and relaxation self-sustained oscillations, are discussed.

The specific form of an uncertainty constant for the Meyer wavelet basis is proposed. The algorithm based on the Ritz method for the spline approximation is used for minimization of this constant. It is shown that algorithm provide a rather good time-frequency localization after few iteration in comparison with the standard choice of a basic function.

The extraction of micellar aggregation numbers by means of applying the mass action law to the concentration dependence of chemical shift are discussed. It is shown that the proposed new logarithmical form is convenient for extraction of the aggregation numbers. The applicability of the Hoppe's subdivision scheme to the NMR sample data processing is proved.

The article focuses on the study of neurscientists that uses qualitative theoretical neuroscience model to understand the dynamics of thousands of coupled neurons.