相关论文: Dynamics of Kuramoto oscillators with time-delayed…
We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency…
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
This paper presents new methods and results on almost global synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any…
The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has…
Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the…
The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
Chimera states have been recently found in a variety of different coupling schemes and geometries. In most cases, the underlying coupling structure is considered to be static, while many realistic systems display significant temporal…
We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to resonance 2:1 is considered in detail. We derive uniformly rotating…
A wide variety of engineered and natural systems are modelled as networks of coupled nonlinear oscillators. In nature, the intrinsic frequencies of these oscillators are not constant in time. Here, we probe the effect of such a temporal…
In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…
The circadian oscillator exhibits remarkably high temporal precision, despite its exposure to several fluctuations. The central mechanism that protects the oscillator from fluctuations is a collective enhancement of precision, where a…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
The synchronization of human networks is essential for our civilization, and understanding the motivations, behavior, and basic parameters that govern the dynamics of human networks is important in many aspects of our lives. Human ensembles…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…