Related papers: Nonlinear phase coupling functions: a numerical st…
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…
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…
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…
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the…
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 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…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously 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.…
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…
Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction…
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…
The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex…
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…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical…
Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling should be small, but one also expects the reduction to be…
We introduce a scalar reduction method for forced or coupled systems with nonlinearities in both heterogeneity and coupling strength. Heterogeneity is formulated as a relatively weak but nonlinear alteration of the vector field(s). The…
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…
A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…