Topological description of periodic structures of an asymmetric nonlinear oscillator

Hegedűs, Ferenc (2017) Topological description of periodic structures of an asymmetric nonlinear oscillator. In: XXXVII Dynamics Days, Dynamics Days Europe International Conference, 5-9 Jun 2017, Szeged.

Preview

Text (Angol nyelvű, nemzetközi konferencia) 2017_DDays_Hegedus.pdf - Accepted Version Download (621kB) | Preview

Abstract

The bifurcation structure of periodic solutions of a harmonically driven asymmetric nonlinear oscillator (Rayleigh–Plesset equation, describing bubble dynamics) is examined. The control parameters were the amplitude and frequency of the driving with frequency values higher than the subharmonic resonance frequency of the system. In the investigated parameter region, the endoskeleton of the bifurcation structure, composed by solutions with low periodicities, can be described by an asymmetric Farey-ordering tree. To each periodic domain, a sub-structure can be associated created by period-n tupling processes, whose topology are governed by a two-sided symmetric Farey tree. Higher order sub-structures apparently exhibit self-similar features.

Actions (login required)

Edit Item