Related papers: Complexity reduction in the 3D Kuramoto model
We investigate the dynamics of a three-dimensional system modeling a molecular mechanism for the circadian rhythm in Drosophila. We first prove the existence of a compact attractor in the region with biological meaning. Under the assumption…
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…
In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…
Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators.…
Super-critical Kuramoto oscillators with distributed frequencies separate into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators -- at least so in the…
Randomly coupled phase oscillators may synchronize into disordered patterns of collective motion. We analyze this transition in a large, fully connected Kuramoto model with symmetric but otherwise independent random interactions. Using the…
A scenario frequently encountered in real-world complex systems is the temporary failure of a few components. For systems whose functionality hinges on the collective dynamics of the interacting components, a viable approach to dealing with…
Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order…
In a system of heterogeneous (Abelian) Kuramoto oscillators with random or `frustrated' interactions, transitions from states of incoherence to partial synchronization were observed. These so-called volcano transitions are characterized by…
We consider a system of globally-coupled phase-only oscillators with distributed intrinsic frequencies and evolving in presence of distributed Gaussian, white noise, namely, a Gaussian, white noise whose strength for every oscillator is a…
We present an extension of the Kuramoto-Sakaguchi model for networks, deriving the second-order phase approximation for a paradigmatic model of oscillatory networks - an ensemble of non-identical Stuart-Landau oscillators coupled pairwisely…
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original,…
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…
We show that the long-range order (LRO) strikingly emerges in systems of locally coupled $D$-dimensional vector Kuramoto oscillators on low-dimensional lattices ($d=1,2$), but only for odd $D$. This parity-dependent effect is traced to…
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…
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…
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…
Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…
We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant…
There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a network like structure. Within the framework of oscillatory models, much attention has…