Related papers: Estimating Phase from Observed Trajectories Using …
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
In this paper, we analyze the asymptotic properties of the Two-Stage (TS) estimator -- a simulation-based parameter estimation method that constructs estimators offline from synthetic data. While TS offers significant computational…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit. Knowledge of this curve yields a phase…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
We show that the phase of a spin-torque oscillator generically acquires a geometric contribution upon slow and cyclic variation of the parameters that govern its dynamics. As an example, we compute the geometric phase that results from a…
In plasma turbulence theory, due to the complexity of the system with many non-linearly interacting waves, the dynamics of the phases is often disregarded and the so-called random-phase approximation (RPA) is used assuming the existence of…
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest…
We elucidate the relation between out-of-time-order correlators (OTOCs) and quantum phase transitions via analytically studying the OTOC dynamics in a degenerate spectrum. Our method points to key ingredients to dynamically detect quantum…
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is…
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring…
We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
An $n$th-order first derivative test for oscillatoric integrals is established. When the phase has a single stationary point, an $n$th-order asymptotic expansion of a weighted stationary phase integral is proved for arbitrary $n\geq1$. This…
We show that a ring of phase oscillators coupled with transmission delays can be used as a pattern recognition system. The introduced model encodes patterns as stable periodic orbits. We present a detailed analysis of the underlying…
We consider the task of estimating the randomly fluctuating phase of a continuous-wave beam of light. Using the theory of quantum parameter estimation, we show that this can be done more accurately when feedback is used (adaptive phase…
A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in…
Circular variables such as phase or orientation have received considerable attention throughout the scientific and engineering communities and have recently been quite prominent in the field of neuroscience. While many analytic techniques…
We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the…