Peculiarities of wave dynamics in media with oscillating inclusions |
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| Institution: | 1. Laboratoire de Mécanique, Département de Physique, Faculté des Sciences, Université de Yaoundé I, Yaoundé B.P. 812, Cameroun;2. Centre d’ Excellence en Technologies de l’ Information et de la Communication (CETIC), Cameroun;3. Botswana International University of Science and Technology, Private Bag 16 Palapye, Botswana;1. National Advanced School of Engineering, University of Yaounde I, P.O. Box 8390, Cameroon;2. Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Cameroon;3. Centre d’Excellence en Technologies de l’Information et de la Communication (CETIC), University of Yaounde I, Yaounde, P.O.Box 8390, Cameroon;4. Laboratory of Research on advanced and nonlinear sciences (LaRAMaNS), Department of physics, faculty of science, University of Buea, Buea, P.O Box 63, Cameroon;5. Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67, Cameroon |
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| Abstract: | 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 quasiperiodic and chaotic regimes. Bifurcations of localized regimes are studied via the Poincaré section technique. |
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| Keywords: | Nonlocal model Chaotic attractor Torus Travelling wave |
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