Energy redistribution in hierarchical systems of oscillators

Abstract

The article deals with the mathematical model for media with hierarchical structure. Using the hamiltonian formalism, the dynamical system describing the state of hierarchically connected structural elements was derived. According to the analysis of the Poincar\'e sections, we found the localized quasi-periodic and chaotic trajectories in the three-level hierarchical model. Moreover, studies of correlation functions shown that the power spectrum for three-level model possesses local maxima characterizing temporal scales with strong correlation. Using the Fourier analysis of the solution's components, we have studied the distribution of energy injected in the system over hierarchical levels. Dynamical phenomena in the multi-level system were studied as well.