Related papers: The Kuramoto Model with Time-Varying Parameters
We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures…
Starting with the overall wave function expression for the electron in an Aharonov-Bohm potential, we derive a version of the Kuramoto Model describing the phase dynamics of the bound state of the quantum mechanical system.
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…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
The asymptotic scaling behavior of the Kuramoto model with finite populations has been notably elusive, despite comprehensive investigations employing both analytical and numerical methods. In this paper, we explore the Kuramoto model with…
From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the…
In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…
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 study a simple one-dimensional model of swarmalators, a generalization of phase oscillators that swarm around in space as well as synchronize internal oscillations in time. Previous studies of the model focused on Kuramoto-type…
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…
The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the…
The circadian oscillator exhibits remarkably high temporal precision, despite its exposure to several fluctuations. The central mechanism that protects the oscillator from fluctuations is a collective enhancement of precision, where a…
Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they…
This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the…
Populations of oscillators are present throughout nature. Very often synchronization is observed in such populations if they are allowed to interact. A paradigmatic model for the study of such phenomena has been the Kuramoto model. However,…
We examine the impact of time delay on two coupled massive oscillators within the second-order Kuramoto model, which is relevant to the operations of real-world networks that rely on signal transmission speed constraints. Our analytical and…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We study the dynamics of a generalized version of the famous Kuramoto-Sakaguchi coupled oscillator model. In the classic version of this system, all oscillators are governed by the same ODE, which depends on the order parameter of the…
We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this…