Related papers: Synchronization of Coupled Kuramoto Oscillators un…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
Recently, there has been significant advancement in the machine learning (ML) approach and its application to diverse systems ranging from complex to quantum systems. As one of such systems, a coupled-oscillators system exhibits intriguing…
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the…
Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal…
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…
We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for…
Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto…
Brain networks typically exhibit characteristic synchronization patterns where several synchronized clusters coexist. On the other hand, neurological disorders are considered to be related to pathological synchronization such as excessive…
Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt coupling strengths between units in accordance with their activity…
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…
The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has…
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…
The Kuramoto model has been introduced to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. The model consists of $N$ interacting oscillators on the one dimensional sphere $\mathbf{S}^{1}$, driven…
We study the collective behavior in a stochastic agent-based model of active matter. Provided a critical take-up of energy, agents produce two types of goods $x$, $y$ that follow a generalized Lotka-Volterra dynamics. For isolated agents,…
Due to its description of a synchronization between oscillators, the Kuramoto model is an ideal choice for a synchronisation algorithm in networked systems. This requires to achieve not only a frequency synchronization but also a phase…
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two…