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Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation…
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…
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of…
We study the kinetic Kuramoto model for coupled oscillators. We prove that for any regular asymptotically free state, if the interaction is small enough, it exists a solution which is asymptotically close to it. For this class of solution…
By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…
The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto…
Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find…
Sparsely coupled Kuramoto oscillators offer a fertile playground for exploring high-dimensional basins of attraction due to their simple yet multistable dynamics. For $n$ identical Kuramoto oscillators on cycle graphs, it is well known that…
Dynamics of complex systems are often driven by interactions that extend beyond pairwise links, underscoring the need to establish a correspondence between interpretable system parameters and emergent phenomena in hypergraph-based networks.…
Disorder is often seen as detrimental to collective dynamics, yet recent work has shown that heterogeneity can enhance network synchronization. However, its constructive role in stabilizing nontrivial cooperative patterns remains largely…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
Synchronization in networks of coupled oscillators is classically studied via the Kuramoto model, whose intrinsic nonlinearity limits analytical tractability and complicates control design. Complex-valued extensions circumvent this by…
The effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We…
We report the appearance of a scroll ring and scroll toroid chimera states from the proposed initial conditions for the Kuramoto model of coupled phase oscillators in the 3D grid topology with inertia. The proposed initial conditions…
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…
Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study a wide range of systems. Despite numerous efforts to…
Exploring the spectrum of novel behaviors a physical system can produce can be a labor-intensive task. Active learning is a collection of iterative sampling techniques developed in response to this challenge. However, these techniques often…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
We consider the existence of non-synchronized fixed points to the Kuramoto model defined on sparse networks: specifically, networks where each vertex has degree exactly three. We show that "most" such networks support multiple attracting…
Collective synchronization is often summarized by a complex order parameter $R e^{i\Psi}$, implicitly treating the global phase $\Psi$ as a meaningful macroscopic coordinate. Here we ask when $\Psi$ becomes \emph{operationally well-defined}…