Towards classification of the bifurcation structure of a spherical cavitation bubble

Classification of the bifurcation structure of a periodically driven gas bubble

“…In this section, we show few examples of these diagrams, and discus that how our results extend Behnia's findings [1].…”

“…Therefore, the bifurcation structure should not change drastically either. In the present paper, this problem is revisited using the same equation, the Keller-Miksis oscillator, as applied by Behnia et al [1]. The detailed analytical and numerical investigations revealed the range of the applicability of Behnia's condition, which is affected by the viscosity and the surface tension.…”

“…The results of Behnia et al [1], however, is a specialty of nonlinear bubble dynamics. They found that the bifurcation structures of different pressure amplitude response curves are remarkably similar when R E ω is kept constant, but detailed physical explanation and range of validity was omitted.…”

“…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.…”

“…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.…”