Related papers: Exponential synchronization of the high-dimensiona…
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…
We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…
The influence of array geometry on synchronization properties of a 2-D oscillator array is investigated based on a comparison between a rectangular and a hexagonal grid. The Kuramoto model is solved for a nearest-neighbor case with periodic…
In this paper, we investigate how the self-synchronization property of a swarm of Kuramoto oscillators can be controlled and exploited to achieve target densities and target phase coherence. In the limit of an infinite number of…
Explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. In the current work, we took into account mean-field approximations to determine the…
The Kuramoto model (KM) is a theoretical paradigm for investigating the emergence of rhythmic activity in large populations of oscillators. A remarkable example of rhythmogenesis is the feedback loop between excitatory (E) and inhibitory…
We show that an introduction of a phase parameter ($\alpha$), with $0 \le \alpha \le \pi/2$, in the interlayer coupling terms of multiplex networks of Kuramoto oscillators can induce explosive synchronization (ES) in the multiplexed layers.…
The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscillatory networks. In this work, we revisit Kuramoto-type…
Explosive synchronization refers to an abrupt (first order) transition to non-zero phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
Despite growing interest in synchronization dynamics over "higher-order" network models, optimization theory for such systems is limited. Here, we study a family of Kuramoto models inspired by algebraic topology in which oscillators are…
The study of frequency synchronization configurations in Kuramoto models is a ubiquitous mathematical problem that has found applications in many seemingly independent fields. In this paper, we focus on networks whose underlying graph are…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
We have examined the synchronization and de-synchronization transitions observable in the Kuramoto model with a standard pair-wise first harmonic interaction plus a higher order (triadic) symmetric interaction for unimodal and bimodal…
Large ensembles of heterogeneous oscillators often exhibit collective synchronization as a result of mutual interactions. If the oscillators have distributed natural frequencies and common shear (or nonisochronicity), the transition from…
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization…
The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…
We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto…