Effective equation for two coupled oscillators: towards a global view of metamorphoses of the amplitude profiles
| Autor: | Andrzej Okninski, Jan Kyzioł |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
34C15 (Primary) 74H10 70K50 (Secondary) Applied Mathematics Mechanical Engineering Dynamics (mechanics) Mathematical analysis FOS: Physical sciences Singular point of a curve Parameter space Nonlinear Sciences - Chaotic Dynamics Nonlinear system Amplitude Mechanics of Materials Chaotic Dynamics (nlin.CD) Bifurcation Effective equation |
| DOI: | 10.48550/arxiv.2004.09236 |
| Popis: | Dynamics of nonlinear coupled driven oscillators is investigated. Recently, we have demonstrated that the amplitude profiles -- dependence of the amplitude $A$ on frequency $\Omega$ of the driving force, computed by asymptotic methods in implicit form as $F\left( A,\Omega \right) =0$, permit prediction of metamorphoses of dynamics which occur at singular points of the implicit curve $F\left( A,\Omega \right) =0$. In the present study we strive at a global view of singular points of the amplitude profiles computing bifurcation sets, i.e. sets containing all points in the parameter space for which the amplitude profile has a singular point. Comment: 17 pages, 14 figures, figures and references added |
| Databáze: | OpenAIRE |
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