Signal-to-pump back-action and self-oscillation in Double-Pump Josephson Parametric Amplifier

We present the theory of a Josephson parametric amplifier employing two pump sources. Our calculations are based on Input-Output Theory, and can easily be generalized to any coupled system involving parametric interactions. We analyze the operation of the device, taking into account the feedback introduced by the reaction of the signal and noise on the pump power, and in this framework, compute the response functions of interest - signal and idler gains, internal gain of the amplifier, and self-oscillation signal amplitude. To account for this back-action between signal and pump, we adopt a mean-field approach and self-consistently explore the boundary between amplification and self-oscillation. The coincidence of bifurcation and self-oscillation thresholds reveals that the origin of coherent emission of the amplifier lies in the multi-wave mixing of the noise components. Incorporation of the back-action leads the system to exhibit hysteresis, dependent on parameters like temperature and detuning from resonance. Our analysis also shows that the resonance condition itself changes in the presence of back-action and this can be understood in terms of the change in plasma frequency of the junction. The potential of the double pump amplifier for quantum-limited measurements and as a squeezer is also discussed.Comment: 25 pages, 20 figures, three appendice

Hysteresis and bi-stability by an interplay of calcium oscillations and action potential firing

Many cell types exhibit oscillatory activity, such as repetitive action potential firing due to the Hodgkin-Huxley dynamics of ion channels in the cell membrane or reveal intracellular inositol triphosphate (IP$_3$) mediated calcium oscillations (CaOs) by calcium-induced calcium release channels (IP$_3$-receptor) in the membrane of the endoplasmic reticulum (ER). The dynamics of the excitable membrane and that of the IP$_3$-mediated CaOs have been the subject of many studies. However, the interaction between the excitable cell membrane and IP$_3$-mediated CaOs, which are coupled by cytosolic calcium which affects the dynamics of both, has not been studied. This study for the first time applied stability analysis to investigate the dynamic behavior of a model, which includes both an excitable membrane and an intracellular IP$_3$-mediated calcium oscillator. Taking the IP$_3$ concentration as a control parameter, the model exhibits a novel rich spectrum of stable and unstable states with hysteresis. The four stable states of the model correspond in detail to previously reported growth-state dependent states of the membrane potential of normal rat kidney fibroblasts in cell culture. The hysteresis is most pronounced for experimentally observed parameter values of the model, suggesting a functional importance of hysteresis. This study shows that the four growth-dependent cell states may not reflect the behavior of cells that have differentiated into different cell types with different properties, but simply reflect four different states of a single cell type, that is characterized by a single model.Comment: 29 pages, 6 figure

Oscillators and relaxation phenomena in Pleistocene climate theory

Ice sheets appeared in the northern hemisphere around 3 million years ago and glacial-interglacial cycles have paced Earth's climate since then. Superimposed on these long glacial cycles comes an intricate pattern of millennial and sub-millennial variability, including Dansgaard-Oeschger and Heinrich events. There are numerous theories about theses oscillations. Here, we review a number of them in order to draw a parallel between climatic concepts and dynamical system concepts, including, in particular, the relaxation oscillator, excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all theories of ice ages reviewed here feature a phenomenon of synchronisation between internal climate dynamics and the astronomical forcing. However, these theories differ in their bifurcation structure and this has an effect on the way the ice age phenomenon could grow 3 million years ago. All theories on rapid events reviewed here rely on the concept of a limit cycle in the ocean circulation, which may be excited by changes in the surface freshwater surface balance. The article also reviews basic effects of stochastic fluctuations on these models, including the phenomenon of phase dispersion, shortening of the limit cycle and stochastic resonance. It concludes with a more personal statement about the potential for inference with simple stochastic dynamical systems in palaeoclimate science. Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages, Dansgaard-Oeschger eventsComment: Published in the Transactions of the Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), as a contribution to the Proceedings of the workshop on Stochastic Methods in Climate Modelling, Newton Institute (23-27 August). Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on request to author and on http://www.uclouvain.be/ito

Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices

Acknowledgements The authors acknowledge the projects supported by the National Basic Research Program of China (973 Project)(No. 2015CB057405) and the National Natural Science Foundation of China (No. 11372082) and the State Scholarship Fund of CSC. DW thanks for the hospitality of the University of Aberdeen.Peer reviewedPostprin

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Bifurcations and singularities for coupled oscillators with inertia and frustration

We prove that any non zero inertia, however small, is able to change the nature of the synchronization transition in Kuramoto-like models, either from continuous to discontinuous, or from discontinuous to continuous. This result is obtained through an unstable manifold expansion in the spirit of J.D. Crawford, which features singularities in the vicinity of the bifurcation. Far from being unwanted artifacts, these singularities actually control the qualitative behavior of the system. Our numerical tests fully support this picture.Comment: 10 pages, 2 figure