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The topology of the stable periodic orbits of a harmonically driven bubble oscillator, the Rayleigh–Plesset equation, in the space of the excitation parameters (pressure amplitude and frequency) has been revealed numerically. This topology is governed by a hierarchy of two-sided Farey trees initiated from a unique primary structure defined also by a simple asymmetric Farey tree. The sub-topology of each of these building blocks is driven by a homoclinic tangency of a periodic saddle. This self-similar organisation is a suitable basis for a general description, since it is in good agreement with partial results obtained in other periodically forced oscillators and iterated maps. The applied ambient pressure in the model is near but still below Blake's critical threshold. Therefore, this paper is also a straightforward continuation of the work of Hegedűs [1] , who first found numerical evidence for the existence of stable, period 1 solutions beyond Blake's threshold. The present findings are crucial for the extension of the available numerical results from period 1 to arbitrary periodicity. [ABSTRACT FROM AUTHOR]

Abstract: Through numerical simulation of the Hoff model we show that when ultrasound contrast agents (UCAs) are excited at frequencies which are close to integer () multiples of their natural resonance frequency, the bifurcation structure of the UCA oscillations as a function of pressure may be characterized by 3 general distinct regions. The UCA behavior starts with initial period one oscillations which undergoes a saddle node bifurcation to m coexisting attractors for an acoustic pressure above a threshold, . Further increasing the pressure above a second threshold , is followed by a sudden transition to period 1 oscillations. [Copyright &y& Elsevier]

Abstract: We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, subject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the otherʼs growth and encourage the otherʼs demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails. [Copyright &y& Elsevier]

Abstract: The Letter presents a number of new bifurcation structures that can be observed when a multi-dimensional period-doubling system is subjected to a periodic forcing. We show how multi-layered tori arise through transverse period-doubling bifurcations of the resonant saddle and node cycles, and how these multi-layered tori transform into period-doubled ergodic tori through sets of saddle–node bifurcations. [Copyright &y& Elsevier]