Route to shrimps: Dissipation driven formation of shrimp-shaped domains

•Phase diagrams of the Keller–Miksis forced bubble oscillator.•Resonance family of the period-3 stable solution.•Dissipation driven formation of shrimp shaped periodic domains. In this paper, two scenarios for the formation of shrimp-shaped domains [1] are presented. The employed test model is the K...

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Bibliographic Details
Published in:	Chaos, solitons and fractals Vol. 130; p. 109424
Main Authors:	Varga, Roxána, Klapcsik, Kálmán, Hegedűs, Ferenc
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.01.2020
Subjects:	Bifurcation structure Bubble dynamics GPU programming High dissipation rate Keller–Miksis equation Shrimp-shaped domains Bubble dynamics High dissipation rate GPU programming Bifurcation structure Shrimp-shaped domains Keller–Miksis equation
ISSN:	0960-0779, 1873-2887
Online Access:	Get full text
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Summary:	•Phase diagrams of the Keller–Miksis forced bubble oscillator.•Resonance family of the period-3 stable solution.•Dissipation driven formation of shrimp shaped periodic domains. In this paper, two scenarios for the formation of shrimp-shaped domains [1] are presented. The employed test model is the Keller–Miksis equation that is a second order, harmonically forced nonlinear oscillator describing the dynamics of a single spherical gas bubble placed in a liquid domain. The results have shown that with an increasing dissipation rate (liquid viscosity), shrimp-shaped domains are evolved within the complex structure of each subharmonic resonances in the amplitude-frequency parameter plane of the external forcing. The mechanism is the coalescence and interaction of two pairs of a period-doubling and a saddle-node codimension-two bifurcation curves.
ISSN:	0960-0779 1873-2887
DOI:	10.1016/j.chaos.2019.109424