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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| Veröffentlicht in: | Chaos, solitons and fractals Jg. 130; S. 109424 |
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| Abstract | •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. |
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| AbstractList | •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. |
| ArticleNumber | 109424 |
| Author | Klapcsik, Kálmán Hegedűs, Ferenc Varga, Roxána |
| Author_xml | – sequence: 1 givenname: Roxána orcidid: 0000-0003-3396-7499 surname: Varga fullname: Varga, Roxána email: rvarga@hds.bme.hu – sequence: 2 givenname: Kálmán surname: Klapcsik fullname: Klapcsik, Kálmán – sequence: 3 givenname: Ferenc orcidid: 0000-0002-8693-1660 surname: Hegedűs fullname: Hegedűs, Ferenc |
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| Keywords | Bubble dynamics High dissipation rate GPU programming Bifurcation structure Shrimp-shaped domains Keller–Miksis equation |
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