Related papers: High-order phase reduction for coupled 2D oscillat…
We consider optimization of linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On…
This article presents proposals for the design of reduced-order controllers for high-dimensional dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational…
A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of…
Networks of phase oscillators can serve as dense associative memories if they incorporate higher-order coupling beyond the classical Kuramoto model's pairwise interactions. Here we introduce a generalized Kuramoto model with combined…
We present a framework for controlling the collective phase of a system of coupled oscillators described by the Kuramoto model under the influence of a periodic external input by combining the methods of dynamical reduction and optimal…
Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. We present a description in terms of phase and amplitude deviation for…
Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. They are also of direct relevance in the context of currently emerging experiments on nano- and optomechanical…
We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and…
We present a method for reconstructing resonant interactions in weakly coupled phase oscillator systems from noisy time series. Instead of attempting to recover the full phase equations, which may be non-identifiable in the presence of…
Phase reduction framework for limit-cycling systems based on isochrons has been used as a powerful tool for analyzing rhythmic phenomena. Recently, the notion of isostables, which complements the isochrons by characterizing amplitudes of…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
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…
We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems…
A universal approach is proposed for suppression of collective synchrony in a large population of interacting rhythmic units. We demonstrate that provided that the internal coupling is weak, stabilization of overall oscillations with…
The particular properties of synchronization are discussed for the system of coupled van der Pol - Duffing oscillators. The arrangement of synchronization tongues and the particular properties of their internal structure in the parameter…
For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but…
The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally-coupled oscillators. The macroscopic phase…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
We introduce a new model consisting of globally coupled high-dimensional generalized limit-cycle oscillators, which explicitly incorporates the role of amplitude dynamics of individual units in the collective dynamics. In the limit of weak…