Related papers: Phase and frequency linear response theory for hyp…
We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
We propose a method for designing two-dimensional limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly-perturbed…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
Fluid flows play a central role in scientific and technological development, and many of these flows are characterized by a dominant oscillation, such as the vortex shedding in the wake of nearly all transportation vehicles. The ability to…
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schr\"{o}dinger equation.…
Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break…
We introduce a numerically exact and computationally feasible nonlinear-response theory developed for lossy superconducting quantum circuits based on a framework of quantum dissipation in a minimally extended state space. Starting from the…
Reaction-diffusion systems can describe a wide class of rhythmic spatiotemporal patterns observed in chemical and biological systems, such as circulating pulses on a ring, oscillating spots, target waves, and rotating spirals. These…
An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator subjected to weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase…
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 develop a linear response theory to provide a unified description of two recent spectroscopy protocols for probing one-dimensional supersolid states realized in cold-atom systems. Both protocols involve applying a periodic optical…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that…
The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex…
We consider simple examples illustrating some new features of the linear response theory developed by Ruelle for dissipative and chaotic systems [{\em J. of Stat. Phys.} {\bf 95} (1999) 393]. In this theory the concepts of linear response,…