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Spectral analytical methods of research of several classes of non-autonomous model systems

A. A. Egorov 1, Yu. A. Konyaev 2, Nguyen Viet Khoa 3
A.M. Prokhorov General Physics Institute of the Russian Academy of Sciences
National Research University “Moscow Power Engineering Institute”
Kien Giang Teacher Training College, Vietnam

 The paper is received on January 18, after correction - on February 17, 2016


Abstract. The presented work is devoted to the development of known mathematical methods, and also working out of new spectral analytical methods and constructive algorithms necessary at the analysis of various theoretical linear and quasi-linear dynamic models, realized in the form of systems of ordinary differential equations with periodic, polynomial and polynomially periodic matrix. Such models are of great importance at studying of some real physical phenomena and processes. The basic attention in work is given to consideration of a spectral variant of the averaging method at the analysis of non-autonomous systems of differential equations with the periodic matrix, describing regularly perturbed systems. Some results of use of the specified methods for research of the specific real physical phenomena representing doubtless practical interest also are resulted in the paper. In particular the interaction of two coupled linear oscillator in the absence of resonance phenomena is analyzed.

Key words: non-autonomous systems, Mathieu equation, parametric resonance, spectral method, differential equations with periodic matrix, study of stability, linear oscillator.