Bifurcation structure of bubble oscillators

Parlitz, Ulrich; Englisch, Volker; Scheffczyk, C.; Lauterborn, Werner

doi:10.1121/1.399855

Cited by 244 publications

(195 citation statements)

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“…The accumulated knowledge of this nonlinear behavior has been summarized in many reviews [18][19][20] and papers [1,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. The most important findings are the existence of period-doubling cascades in the bifurcation structure [1,21,30,31,35], the appearance of resonance horns in the amplitude-frequency plane of the driving [24,27,34] or the alternation of chaotic and periodic windows [21,23,33]. These structures show similarities with the results obtained on other nonlinear oscillators such as Toda [37], Duffing [38][39][40][41] and others [42], implying that they are universal features of nonlinear systems rather than unique properties of oscillating bubbles.…”

Section: Introductionmentioning

confidence: 99%

Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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The bifurcation structure of a periodically driven spherical gas/vapour bubble is examined by means of methods of nonlinear analysis. The study of Behnia and his coworkers [1] revealed that the bifurcation structures with the pressure amplitude of the excitation as control parameter are structurally similar provided that R E ω is kept constant. In the present paper, this problem is revisited. Analytical and numerical investigations of the bubble oscillator, which is the Keller-Miksis equation, are presented. It is shown that the validity range of Behnia's condition is governed by the viscosity and the surface tension, and holds only for relatively large bubbles. In water, the effect of viscosity is negligible, and the surface tension plays significant role at bubble size lower than approximately 5 µm.

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Section: Introductionmentioning

confidence: 99%

Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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“…This happens because the basins of the attractors deform under the change of the parameters of equation (1). If such a change is large enough, a point which was in a small neighborhood of one of the coexisting attractors can appear in the basin of another attractor at the next value of the parameter.…”

Section: Main Equation and Resultsmentioning

confidence: 99%

“…Let us numerically investigate the dynamics of the gas bubbles governed by equation (1). An attractor is called hidden if its basin of attraction does not intersect with small neighborhoods of equilibria.…”

Section: Main Equation and Resultsmentioning

confidence: 99%

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Hidden Attractors in a Model of a Bubble Contrast Agent Oscillating Near an Elastic Wall

2018

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Abstract.A model describing the dynamics of a spherical gas bubble in a compressible viscous liquid is studied. The bubble is oscillating close to an elastic wall of finite thickness under the influence of an external pressure field which simulates a contrast agent oscillating close to a blood vessel wall. Here we investigate numerically the coexistence of chaotic and periodic attractors in this model. One of the tools applied for seeking coexisting attractors is the perpetual points method. This method can be helpful for localizing coexisting attractors, occurring in various physically realistic ranges of variation of the control parameters. We provide some examples of coexisting attractors to demonstrate the importance of the multistability problem for the applications.

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“…This method continued through increasing the control parameter and the new resulting discrete points were plotted in the bifurcation diagram versus the new control parameter. For a full discussion on the bifurcation diagram and Lyapunov exponent spectrum, their utilization in order to study the bubble dynamics, one can refer to [43,44].…”

Section: Bifurcation Diagramsmentioning

confidence: 99%

Chaotic behavior of gas bubble in non-Newtonian fluid: a numerical study

et al. 2013

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In the present paper, the nonlinear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. Due to the importance of the bubble in the medical applications such as drug, protein or gene delivery, blood is assumed to be the reference fluid. Effects of viscoelasticity term, Deborah number, amplitude and frequency of the acoustic pulse are studied. We have studied the dynamic behavior of the radial response of bubble using Lyapunov exponent spectra, bifurcation diagrams, time series and phase diagram. A period-doubling bifurcation structure is predicted to occur for certain values of the effects of parameters. The results show that by increasing the elasticity of the fluid, the growth phenomenon will be unstable. On the other hand, when the frequency of the external pulse increases the bubble growth experiences more stable condition. It is shown that the results are in good agreement with the previous studies.

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Bifurcation structure of bubble oscillators

Cited by 244 publications

References 0 publications

Classification of the bifurcation structure of a periodically driven gas bubble

Classification of the bifurcation structure of a periodically driven gas bubble

Hidden Attractors in a Model of a Bubble Contrast Agent Oscillating Near an Elastic Wall

Chaotic behavior of gas bubble in non-Newtonian fluid: a numerical study

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