TAILIEUCHUNG - A new approach to the theory of hierarchic wave-oscillation dynamic systems
A new approach to the theory of hierarchic wave-oscillation dynamic systems. A set of new ideas and concepts (which the authors treat as a new version of the theory of hierarchic dynamic systems) are set forth in the article. In turn, the set of hierarchic principles is put in the methodogical basis of this theory. | Communications in Physics, Vol. 19, No. 1 (2009), pp. 9-18 A NEW APPROACH TO THE THEORY OF HIERARCHIC WAVE-OSCILLATION DYNAMIC SYSTEMS V. V. KULISH, I. V. GUBANOV Department of Theoretical Physics, National Aviation University, 1 Kosmonavta Komarova Prospect, 03058, Kyiv, Ukraine LE HUU DIEN, NGUYEN AI VIET Institute of Physics and Electronics, VAST O. V. LYSENKO Department of Theoretical Physics, Sumy State University, 2 Rymskii-Korsakov Str., 44007, Sumy, Ukraine Abstract. A set of new ideas and concepts (which the authors treat as a new version of the theory of hierarchic dynamic systems) are set forth in the article. In turn, the set of hierarchic principles is put in the methodogical basis of this theory. It is shown, a peculiar version of the theory of hierarchic waves and oscillations can be developed on the basis of proposed general theory. I. INTRODUCTION As it is well known, a conventional version of the theory of hierarchic dynamic systems (see [1-5]) is most popular now. Another (new) version of the hierarchic approach has been proposed in monographs [6-9] and papers [10-13]. When a proper set of dynamical variables for each hierarchic level is introduced, therein, the proper variables are chosen in such a way that the mathematical structure of the dynamic equations for every hierarchic level (in these new variables) is the same. Hence, essentially new basic concepts are used in the proposed version of hierarchic theory. Further development of such theory is undertaked in this work. The main attention is given to the nonlinear wave-oscillation dynamic systems with explicitly expressed hierarchy of periods (frequencies) of oscillations. Let us begin with discussion of the set of hierarchic principles that are put into basis of the theory considered. These principles [7-13] originate from relevant generalization of totality of experimental facts and observations well known today. II. HIERARCHIC PRINCIPLES The five following hierarchic principles form a
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