Related papers: Evolutionary Kuramoto Dynamics
We present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [{\it Chemical Oscillations, Waves, and Turbulence}, Springer-Verlag (1984)], a prototype model for coupled…
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…
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show…
Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…
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…
We generalize the Kuramoto model by interpreting the $N$ variables on the unit circle as eigenvalues of a $N$-dimensional unitary matrix $U$, in three versions: general unitary, symmetric unitary and special orthogonal. The time evolution…
Motivated by phenomena related to biological systems such as the synchronously flashing swarms of fireflies, we investigate a network of phase oscillators evolving under the generalized Kuramoto model with inertia. A distance-dependent,…
We explore the impact of global resetting on Kuramoto-type models of coupled limit-cycle oscillators with distributed frequencies both in absence and presence of noise. The dynamics comprises repeated interruption of the bare dynamics at…
The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…
We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…
When modeling the classical Kuramoto model, one of the key features is the tendency to synchronize. Accordingly, the most well-adopted choice of the coupling function is the sine function. Due to the oddness of the sine function, the…
We introduce a new model consisting of globally coupled high-dimensional generalized limit-cycle oscillators, which explicitly incorporates the role of amplitude dynamics of individual units in the collective dynamics. In the limit of weak…
We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…
We study the noisy Kuramoto model for two interacting communities of oscillators, where we allow the interaction in and between communities to be positive or negative (but not zero). We find that, in the thermodynamic limit where the size…
Models of learning typically focus on synaptic plasticity. However, learning is the result of both synaptic and myelin plasticity. Specifically, synaptic changes often co-occur and interact with myelin changes, leading to complex dynamic…
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models,…
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…
Networks of phase oscillators can serve as dense associative memories if they incorporate higher-order coupling beyond the classical Kuramoto model's pairwise interactions. Here we introduce a generalized Kuramoto model with combined…
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions remain on the solutions for systems composed of coupled Kuramoto…
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…