Peculiarities of wave dynamics in media with oscillating inclusions

摘要

The article is concerned with mathematical models for media with oscillating inclusions. These models consist of mutually connected equations, one of which is the wave equation for carrying medium and others are equations of motion for partial oscillators. To close these models, we use cubic and nonlocal equations of state for the carrying medium. Travelling wave solutions to these models are studied in detail. Using qualitative analysis methods, the phase space is shown to contain periodic, homo- and heteroclinic trajectories. Moreover, in the case of nonlocal models we observe the creation of quasi periodic and chaotic regimes. Bifurcations of localized regimes are studied via the Poincare section technique. (C) 2016 Elsevier Ltd. All rights reserved.