Related papers: Phase reduction explains chimera shape: when multi…
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
Real-world networks are often characterized by simultaneous interactions between multiple agents that adapt themselves due to feedback from the environment. In this article, we investigate the dynamics of an adaptive multilayer network of…
We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…
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…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small…
A complex collective emerging behavior characterized by coexisting coherent and incoherent do- mains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators…
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…
There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a network like structure. Within the framework of oscillatory models, much attention has…
We study a simple one-dimensional model of swarmalators, a generalization of phase oscillators that swarm around in space as well as synchronize internal oscillations in time. Previous studies of the model focused on Kuramoto-type…
In this work, we study the inertial Kuramoto model, which is a second-order extension of the classical first-order Kuramoto model, as an inertial perturbation of the first-order Kuramoto model. We develop a quantitative Tikhonov theorem,…
In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…
Understanding how higher-order interactions shape the energy landscape of coupled oscillator networks is crucial for characterizing complex synchronization phenomena. Here, we investigate a generalized Kuramoto model with triadic…
Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto…
The Kuramoto model of coupled phase oscillators with inertia on Erdos-Renyi graphs is analyzed in this work. For a system with intrinsic frequencies sampled from a bimodal distribution we identify a variety of two cluster patterns and study…
Networks in nature have complex interactions among agents. One significant phenomenon induced by interactions is synchronization of coupled agents, and the interactive network topology can be tuned to optimize synchronization. The previous…
A bifurcation from the incoherent state to the partially synchronized state of the Kuramoto-Daido model with the coupling function $f(\theta ) = \sin (\theta +\alpha _1) + h\sin 2(\theta +\alpha _2)$ is investigated based on the generalized…
This paper proposes a novel second order mathematical model in the Kuramoto framework to simulate and study low frequency oscillations in power systems. This model facilitates better understanding of the complex dynamics of a power network.…
We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the…