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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…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
We study information scrambling, as diagnosed by the out-of-time order correlations (OTOCs), in a system of large spins collectively interacting via spatially inhomogeneous and incommensurate exchange couplings. The model is realisable in a…
The techniques of cavity optomechanics have enabled significant achievements in precision sensing, including the detection of gravitational waves and the cooling of mechanical systems to their quantum ground state. Recently, the inherent…
We report the experimental implementation of the Dicke model in the semiclassical approximation, which describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This…
This is the last part of four series papers, aiming at stabilization for signal-input-signaloutput (SISO) linear finite-dimensional systems corrupted by general input disturbances. A new observer, referred to as Extended Dynamics Observer…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…
A detailed description is provided of a numerical model of the microcavity optical parametric oscillator (OPO). The model is solved on a two dimensional grid, in the time domain, using an alternating-direction implicit method. Results are…
Injection-locked ring oscillators (ILROs) are extensively employed for multi-phase clock generation in wireline and optical links. However, existing injection-locking theorems primarily rely on linearized phase-domain or nonlinear…
Delay-Doppler multiplexing has recently stirred a great deal of attention in research community. While multiple studies have investigated pulse-shaping aspects of this technology, it is challenging to identify the relationships between…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
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…
This paper deals with the numerical integration of well-posed multiscale systems of ODEs or evolutionary PDEs. As these systems appear naturally in engineering problems, time-subcycling techniques are widely used every day to improve…
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator…
This is the first part of four series papers, aiming at the problem of actuator dynamics compensation for linear systems. We consider the stabilization of a type of cascade abstract linear systems which model the actuator dynamics…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase…
Microresonator-based degenerate optical parametric oscillation (DOPO) has recently been explored as a compelling platform for all-optical computing and quantum information applications, such as truly random number generation and the…
The spin-boson model, involving spins interacting with a bath of quantum harmonic oscillators, is a widely used representation of open quantum systems. Trapped ions present a natural platform for simulating the quantum dynamics of such…