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We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…

We present the first experimental confirmation of the so-called "self-phaselocked delay interferometry". This laser frequency stabilization technique consists basically in comparing the prompt laser signal with a delayed version of itself…

In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired in the process of learning of birdsong by oscine birds. An oscillator acts as the…

Optomechanical oscillators (OMOs) combine the co-existing high quality factor mechanical and optical resonances in an integrated device to realize low phase noise RF oscillations. While several attempts have been demonstrated towards…

Electromagnetically induced transparency has great theoretical and experimental importance in many physics subjects, such as atomic physics, quantum optics, and more recent cavity optomechanics. Optical delay is the most prominent feature…

The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the…

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…

Optical isolators are indispensable components of optical networks. Magneto-optic isolators have excellent operating characteristics, including low-to-no power consumption, but are not well suited for on-chip integration. The technique of…

There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…

Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial…

Recently, oscillator-based Boolean computation has been proposed for its potentials in noise immunity and energy efficiency. In such a system, logic bits are encoded in the relative phases of oscillating signals and stored in…

A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators…

Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…

In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…

Laser diodes with optical feedback can exhibit periodic intensity oscillations at or near the relaxation-oscillation frequency. We demonstrate optoelectronic oscillators based on external-cavity semiconductor lasers in a periodic dynamical…

Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in…

Narrow-linewidth yet tunable laser oscillators are one of the most important tools for precision metrology, optical atomic clocks, sensing and quantum computing. Commonly used tunable coherent oscillators are based on stimulated emission or…

We report on the realization of an optical phase noise cancellation technique by passively embedding the optical phase information into a radio frequency (RF) signal and shifting the optical frequency with the amount of phase noise…