The phenomenon of self-synchronization in populations of oscillatory units appears naturally in neurosciences. However, in some situations, the formation of a coherent state is damaging. In this article we study a repulsive mean-field Kuramoto model that describes the time evolution of n points on the unit circle, which are transformed into incoherent phase-locked states. It has been recently s...

We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto model on uncorrelated complex networks with scale-free degree distributions. Using the Ott-Antonsen method and the annealed-network approach, we find that the critical behavior of the relaxation rate near the synchronization phase transition does not depend on network heterogeneity and critical slowing down take...

We present synchronization and contractivity estimates for the kinetic Kuramoto model obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto oscillators, we present an admissible class of initial data leading to time-asymptotic complete synchronization, that is, all measure valued solutions converge to the traveling Dirac measure concentrated on the initial avera...

Organizations can be modeled as complex systems. Here we consider complex economic organizations such as the stock exchange and show that the Kuramoto equation is a suitable model to forecast maxima or minima of the financial signals.

We apply the method of self-consistent bounds to prove the existence of multiple steady state bifurcations for Kuramoto-Sivashinski PDE on the line with odd and periodic boundary conditions.

Submitted for the MAR09 Meeting of The American Physical Society Evolution of a Large Fermi Surface in the Kondo Lattice JUNYA OTSUKI, Tohoku University, HIROAKI KUSUNOSE, Ehime University, YOSHIO KURAMOTO, Tohoku University — We investigate the Kondo lattice model with use of the continuous-time quantum Monte Carlo method, combined with the dynamical mean-field theory. The antiferromagnetic ph...

Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, ...

The continuous and discrete symmetries of the Kuramoto–Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaotic dynamics. The continuous spatial translation symmetry leads to relative equilibrium (traveling wave) and relative periodic orbit (modulated traveling wave) solutions. The discrete symmetries lead to existence of eq...

The continuous and discrete symmetries of the Kuramoto-Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its spatiotemporally chaotic dynamics. The continuous spatial translation symmetry leads to relative equilibria (traveling wave) and relative periodic orbit solutions. The discrete symmetries lead to existence of equilibrium a...

There are numerous examples of studied real-world systems that can be described as dynamical characterized by individual phases and coupled in a network like structure. Within the framework oscillatory models, much attention has been devoted to Kuramoto model, which considers collection oscillators interacting through sinus function phase differences. In this paper, we draw on an extension call...