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A two-component reaction-diffusion system modelling a prey-predator system is considered. A necessary condition and a sufficient condition for the internal stabilizability to zero of one the two components of the solution while preserving the nonnegativity of both components have been established by Aniţa. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization corresponding to the indicated feedback control depends on the principal eigenvalue of a certain elliptic operator. A large principal eigenvalue leads to a fast stabilization. The first goal of this paper is to approximate this principal eigenvalue. The second goal is to derive a conceptual iterative algorithm to improve at each iteration the position of the support of the stabilizing control in order to get a faster stabilization.
This work describes a specially developed software for controllable magnetic hysteresis measurements of amorphous and nanocrystalline ribbons. The sophisticated algorithm enables to simplify a hardware design and to suppress an influence of experimental conditions on the measurement results. The main software feature is a three-stage feedback algorithm, which accurately adjusts the magnetization conditions: magnetization amplitude, geomagnetic bias and magnetization waveform. Air flux compensation of the induction signal is also performed by the software using an effective value of the coil cross section obtained from a calibration measurement without the ribbon. Applicability of the designed setup is illustrated for a series of nanocrystalline Hitperm ribbons measured at the power-line conditions: 50 Hz frequency and sinusoidal magnetization waveform.
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