This article is cited in 1 paper

Normal mode spectra of hierarchical ensembles of interconnected oscillators

O. S. Safina^ab, A. V. Voronov^a, A. R. Safin^ac, M. F. Bulatov^b, D. V. Churikov^bc, E. D. Surovyatkina<sup>de

a</sup> National Research University "Moscow Power Engineering Institute"
^b Scientific and Technological Centre of Unique Instrumentation, Russian Academy of Sciences
^c Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow
^d Space Research Institute, Russian Academy of Sciences, Moscow
^e Potsdam Institute for Climate Impact Research, Potsdam, Germany

Abstract: A family of normal mode spectra of hierarchically organized ensembles of identical interconnected oscillators with different topology of the organization is constructed. It is shown that treelike ensembles possess a devil’s-staircase-type fractal spectrum of normal modes; the number of degenerate modes increases with an increase in the number of tree branches and with introduction of additional connections between elements of the ensemble. The effect of ensemble topologies and bond strengths between elements of the ensemble on spectral characteristics is analyzed.

Keywords: oscillators, normal modes, nonlinear oscillations, fractals.

Received: 24.12.2018
Revised: 24.12.2018
Accepted: 29.05.2019

DOI: 10.21883/PJTF.2019.17.48219.17651

 English version: Technical Physics Letters, 2019, 45:9, 874–877

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