Related papers: Connecting the Kuramoto Model and the Chimera Stat…
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…
In a recent study of chaos synchronization in symmetric complex networks [Pecora \textit{et al}., Nat. Commun. {\bf 5}, 4079 (2014)], it is found that stable synchronous clusters may coexist with many non-synchronous nodes in the…
The coexistence of coherent and incoherent domains, namely the appearance of chimera states, is being studied extensively in many contexts of science and technology since the past decade, though the previous studies are mostly built on the…
The phenomenon of self-synchronization in populations of oscillatory units appears naturally in neurosciences. However, in some situations, the formation of a coherent state is damaging. In this article we study a repulsive mean-field…
Study of collective phenomenon in populations of coupled oscillators are a subject of intense exploration in physical, biological, neuronal and social systems. Here we propose a scheme for the creation of chimera states, namely the…
The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…
We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…
Many dynamical systems operate in a fluctuating environment. However, even in low-dimensional setups, transitions and bifurcations have not yet been fully understood. In this Letter we focus on crises, a sudden flooding of the phase space…
We consider an adaptive network, whose connection weights co-evolve in congruence with the dynamical states of the local nodes that are under the influence of an external stimulus. The adaptive dynamical system mimics the adaptive synaptic…
In this work we present a method to control chimera states through linear augmentation. Using an ensemble of globally coupled oscillators, we demonstrate that control over the spatial location of the incoherent or coherent regions of a…
Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such…
Systems of coupled oscillators have been seen to exhibit chimera states, i.e. states where the system splits into two groups where one group is phase locked and the other is phase randomized. In this work, we report the existence of chimera…
Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to the co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial…
We demonstrate the existence of a multiplicity of co-existing frequency combs in a harmonically mode-locked laser that we link to the splay phases of the Kuramoto model with short range interactions. These splay states are multistable and…
This review offers a retrospective of the development of the theory of coupled oscillators and synchronization over the past half century. Among the various works made by myself during this period, the following three specific works will be…
In many real-life situations, individuals are dared to simultaneously achieve social objectives of acceptance or approval and strategic objectives of coordination. Since these two objectives may take place in dfferent environments, a…
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…
The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…