Route to shrimps: Dissipation driven formation of shrimp-shaped domains - Varga, Roxána; Klapcsik, Kálmán; Hegedűs, Ferenc (Chaos, solitons and fractals, 2020)
•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.