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Optomechanical systems subjected to environmental noise give rise to rich physical phenomena. We investigate entanglement between a mechanical oscillator and the reflected coherent optical field in a general, not necessarily Markovian…
Financial spillovers in interconnected systems, such as global banking networks, require tools that capture temporal and frequency dynamics, while incorporating the underlying network topology. While current network time series models are…
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
In this contribution we aim to study the stability boundaries of solutions at equilibria for a second-order oscillator networks with SN-symmetry, we look for non-degenerate Hopf bifurcations as the time-delay between nodes increases. The…
If a disturbance rocks a low-inertia power system, the frequency decline may be too rapid to arrest before it triggers undesirable responses from generators and loads. In the worst case, this instability could lead to blackout and major…
We introduce an efficient numerical method for second order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory…
This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory…
We study the Floquet phase diagram of two-dimensional Dirac materials such as graphene and the one-dimensional (1D) spin-1/2 $XY$ model in a transverse field in the presence of periodic time-varying terms in their Hamiltonians in the low…
This letter concerns the reliability of coupled oscillator networks in response to fluctuating inputs. Reliability means that (following a transient) an input elicits identical responses upon repeated presentations, regardless of the…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phase-oscillator's natural…
Oscillatory reconnection is a time-dependent magnetic reconnection mechanism that naturally produces periodic outputs from aperiodic drivers. This paper aims to quantify and measure the periodic nature of oscillatory reconnection for the…
We derive a time-domain mean-field equation to model the full temporal and spectral dynamics of light in singly resonant cavity-enhanced second-harmonic generation systems. We show that the temporal walk-off between the fundamental and the…
We report on methods to monitor the transmission path in optical networks using a correlation-based OTDR technique with direct and coherent detection. A high probing symbol rate can provide picosecond-accuracy of the fiber propagation…
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…
Spectral behaviors of photonic resonators have been the basis for a range of fundamental studies, with applications in classical and quantum technologies. Driven nonlinear resonators provide a fertile ground for phenomena related to phase…
The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…
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,…