Related papers: High-order phase reduction for coupled 2D oscillat…
We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to…
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.…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic…
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…
An overview is given on two representative methods of dynamical reduction known as center-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion than the theories in the past. The target…
Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for…
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…
Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple…
Low-dimensional reduction theories, such as the Ott-Antonsen ansatz, have played a crucial role in the study of populations of globally coupled phase oscillators. However, most of these theories are applicable only to models in which the…
The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of…
Phase reduction is a powerful technique that makes possible describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…