Related papers: Evolutionary Kuramoto Dynamics
Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role…
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…
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical…
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…
How do the combined effects of phase frustration, noise, and higher-order interactions govern synchronization in globally coupled heterogeneous Kuramoto oscillators? To address this question, we investigate a globally coupled network of…
The Kuramoto model is a system of nonlinear differential equations that models networks of coupled oscillators and is often used to study synchronization among them. It has been observed that if the natural frequencies of the oscillators…
In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays.…
We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…
Higher-order networks with multiway interactions can exhibit collective dynamical phenomena that are absent in traditional pairwise network models. However, analyzing such dynamics becomes computationally prohibitive as their state space…
In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…
We investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as…
Interaction within an ensemble of coupled nonlinear oscillators induces a variety of collective behaviors. One of the most fascinating is a chimera state which manifests the coexistence of spatially distinct populations of coherent and…
We propose a novel model of oscillatory chains that generalizes the contour discrete model of Buslaev nets. The model offers a continuous description of conflicts in system dynamics, interpreted as interactions between neighboring…
We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of…
A small-world network (SW) of similar phase oscillators, interacting according to the Kuramoto model is studied numerically. It is shown that deterministic Kuramoto dynamics on the SW networks has various stable stationary states. This can…
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 general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
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.…
Despite being under intense scrutiny for 50 years, the Kuramoto oscillator model has remained a quintessential representative of non-equilibrium phase transitions. One of the reasons for its enduring relevance is the apparent lack of an…
We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence…