Coupled-Oscillator Associative Memory Array Operation for Pattern Recognition

Operation of the array of coupled oscillators underlying the associative memory function is demonstrated for various interconnection schemes (cross-connect, star phase keying and star frequency keying) and various physical implementation of oscillators (van der Pol, phase-locked loop, spin torque). The speed of synchronization of oscillators and the evolution of the degree of matching is studied as a function of device parameters. The dependence of errors in association on the number of the memorized patterns and the distance between the test and the memorized pattern is determined for Palm, Furber and Hopfield association algorithms

Noise Induces Hopping between NF-kappa B Entrainment Modes

Oscillations and noise drive many processes in biology, but how both affect the activity of the transcription factor nuclear factor κB (NF-κB) is not understood. Here, we observe that when NF-κB oscillations are entrained by periodic tumor necrosis factor (TNF) inputs in experiments, NF-κB exhibits jumps between frequency modes, a phenomenon we call “cellular mode-hopping.” By comparing stochastic simulations of NF-κB oscillations to deterministic simulations conducted inside and outside the chaotic regime of parameter space, we show that noise facilitates mode-hopping in all regimes. However, when the deterministic system is driven by chaotic dynamics, hops between modes are erratic and short-lived, whereas in experiments, the system spends several periods in one entrainment mode before hopping and rarely visits more than two modes. The experimental behavior matches our simulations of noise-induced mode-hopping outside the chaotic regime. We suggest that mode-hopping is a mechanism by which different NF-κB-dependent genes under frequency control can be expressed at different times.ISSN:2405-472

Bistability and Phase Synchronisation in Coupled Quantum Systems

In this work, we investigate novel phase synchronisation features that occur in bistable oscillators, explored with trapped ions and oscillator-only systems, as well as in networks of spin-1 oscillators of varying size and geometry. We begin with two coupled trapped ions each driven by a two-quanta gain process whose dynamical states heavily influence the emergent relative phase preference. Large gain rates produce limit-cycle states where photon numbers can become large with relative phase distributions that are π-periodic with peaks at 0 and π, as extensively discussed in the literature. When the gain rate is low, however, the oscillators have very low photon occupation numbers which produces π-periodic distributions with peaks at π/2 and 3π/2. We find bistability between these limiting cases with a coexistence of limit-cycle and low-occupation states where the relative phase distribution can have π/2 periodicity. These results reveal that synchronisation manifests differently in quantum oscillators outside of the limit-cycle regime. Next, we investigate the origin of these features by proposing a minimal oscillator-only model that also exhibits bistability but with reduced complexity. Our model of two 321 oscillators is purely dissipative, with a two-photon gain balanced by single- and three-photon loss processes. Perturbation theory reveals that the values of π/2 and 3π/2 are due to the form of the number distribution that is produced by the two-quanta gain, unseen in thermal and van der Pol oscillators. Moving away from exploring bistability, we turn our attention to synchronisation in spin-1 oscillators which allows for the simulation of large networks. We derive an analytic form of the relative phase distribution of two spin-1 oscillators in a network that depends on only two complex values. The size and geometry of the network greatly affects the strength and form of synchronisation in the system. A strengthening of the synchronisation between next-nearest neighbours, compared to neighbours, is observed in chain and ring networks of three and four spins

Self-oscillation

Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain dynamical systems that gives rise to a great variety of vibrations, both useful and destructive. In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration: no external rate needs to be adjusted to the resonant frequency. The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the swaying of the London Millennium Footbridge in 2000. Clocks are self-oscillators, as are bowed and wind musical instruments. The heart is a "relaxation oscillator," i.e., a non-sinusoidal self-oscillator whose period is determined by sudden, nonlinear switching at thresholds. We review the general criterion that determines whether a linear system can self-oscillate. We then describe the limiting cycles of the simplest nonlinear self-oscillators, as well as the ability of two or more coupled self-oscillators to become spontaneously synchronized ("entrained"). We characterize the operation of motors as self-oscillation and prove a theorem about their limit efficiency, of which Carnot's theorem for heat engines appears as a special case. We briefly discuss how self-oscillation applies to servomechanisms, Cepheid variable stars, lasers, and the macroeconomic business cycle, among other applications. Our emphasis throughout is on the energetics of self-oscillation, often neglected by the literature on nonlinear dynamical systems.Comment: 68 pages, 33 figures. v4: Typos fixed and other minor adjustments. To appear in Physics Report