Web4 COMPLETELY DEGENERATE EQUILIBRIA OF THE KURAMOTO MODEL ON NETWORKS Figure 2. Blue, green, red and yellow denote 0, p/2, p and 3p/2 respectively. Proposition 5. … Web28 Jul 2024 · The Kuramoto Model [11, 12], which provides a simple theoretical framework to study how synchronization may emerge spontaneously in the dynamics of a many-body interacting system. This model is widely used in biology to study the behavior of very different systems, including fireflies and even neurons.
Optimizing synchronization stability of the Kuramoto model in …
Web13 Jan 2024 · Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the … WebFrom a theoretical perspective, the Kuramoto model has deep connections to effects present in Hamiltonian systems, particularly to Landau damping [11, 12] and bifurcations … christiane pook
The mathematics of asymptotic stability in the Kuramoto model ...
Web12 Oct 2024 · The Kuramoto model consists of an ensemble of all-to-all coupled oscillators with randomly distributed natural frequencies. The coupling between each pair of … Web10 May 2024 · For the Kuramoto model on small-world graphs, in addition to the transition to synchronization, we identify a new bifurcation leading to stable random twisted states. The examples analyzed in this work complement the results in [Chiba, Medvedev, The mean field analysis for the Kuramoto model on graphs (parts I and II), arxiv]. The Kuramoto model (or Kuramoto–Daido model), first proposed by Yoshiki Kuramoto (蔵本 由紀, Kuramoto Yoshiki), is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated by the … See more The transformation that allows this model to be solved exactly (at least in the N → ∞ limit) is as follows: Define the "order" parameters r and ψ as Here r represents … See more The incoherent state with all oscillators drifting randomly corresponds to the solution $${\displaystyle \rho =1/(2\pi )}$$. In that case $${\displaystyle r=0}$$, and there is no … See more There are a number of types of variations that can be applied to the original model presented above. Some models change to topological structure, others allow for heterogeneous weights, and other changes are more related to models that are inspired by the … See more The dissipative Kuramoto model is contained in certain conservative Hamiltonian systems with Hamiltonian of the form See more • pyclustering library includes a Python and C++ implementation of the Kuramoto model and its modifications. Also the library consists of oscillatory networks (for cluster analysis, … See more • Master stability function • Oscillatory neural network • Phase-locked loop See more christiane polduwe