We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparametersensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory.Coupled oscillator systems exhibit a variety of phenomena relevant to physics, biology, and other branches of science and technology. Here, we study oscillation death (OD) [1], a form of synchronization [2] in which the oscillators interact in such a way as to quench each other's oscillations [3][4][5][6]. This intriguing phenomenon was noted in the 19th century by Rayleigh [2], who found that adjacent organ pipes of the same pitch can reduce each other to silence. Since then, OD has been studied in diverse applications including oceanography [7], chemical engineering [8], solid-state lasers [9] and a variety of other experimental systems [4,[10][11][12]. OD is known to occur via two distinct bifurcation mechanisms: (i) Hopf bifurcation, where the coupling induces stability at the origin of the phase space, thus collapsing the orbits to zero, which can happen only if the oscillators are sufficiently different [5,[13][14][15][16] (or for identical oscillators if there are delays [17,18] in the coupling); or (ii) for non-identical oscillators, saddle-node bifurcation [4] in which new fixed points appear on/near the coupled limit cycles, annihilating the periodic orbits. Recently, Karnatak et al. [19] were able to produce OD in two identical coupled oscillators through the saddlenode route, using dissimilar non-delayed coupling.In this Letter, we show that a coupled-oscillator system, which has been used extensively in modeling coupled rhythmic processes in mathematics, physics and biology [26] can undergo OD via both bifurcation routes. We obtain exact analytic conditions for OD, and compare the theory with numerical simulations and analogue electronic experiments. We thus generalize OD as a phenomenon that occurs, not only through coupling-increased dissipativity [2], but also when a measure of dispersion among the parameters of the coupled system is exceeded [21]. We also show that, near the onset of death, the coupled system PACS 82.40.Bj -Oscillations, chaos, and bifurcations PACS 05.45.Xt -Synchronization; coupled oscillators PACS 05.45.-a -Nonlinear dynamics and chaos

The FAMU experiment aims to measure for the first time the hyperfine splitting of the muonic hydrogen ground state. From this measurement the proton Zemach radius can be derived and this will shed light on the determination of the proton charge radius. In this paper, we describe the scientific goal, the method and the detailed preparatory work. This includes the outcome of preliminary measurements, subsequent refined simulations and the evaluation of the expected results. The experimental setup being built for the measurement of the hyperfine splitting to be performed at the RAL laboratory muon facility is also described.

We describe a new technique which minimizes the amount of neurons in the hidden layer of a random recurrent neural network (rRNN) for time series prediction. Merging Takens-based attractor reconstruction methods with machine learning, we identify a mechanism for feature extraction that can be leveraged to lower the network size. We obtain criteria specific to the particular prediction task and derive the scaling law of the prediction error. The consequences of our theory are demonstrated by designing a Takens-inspired hybrid processor, which extends a rRNN with a priori designed delay external memory. Our hybrid architecture is therefore designed including both, real and virtual nodes. Via this symbiosis, we show performance of the hybrid processor by stabilizing an arrhythmic neural model. Thanks to our obtained design rules, we can reduce the stabilizing neural network's size by a factor of 15 with respect to a standard system. PACS numbers: May be entered using the \pacs{#1} command.