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...

A shock-like structure appears in a time-averaged pattern produced by the Kuramoto-Sivashinsky equation and the noisy Burgers equation with fixed boundary conditions. We show that the effective viscosity computed from the width of the time-averaged shock structure is consistent with that computed from the time correlation of the fluctuations. The effective viscosity depends on the lengthscale, ...

Most evolution equations are partially integrable and, in order to explicitly integrate all possible cases, there exist several methods of complex analysis, but none is optimal. The theory of Nevanlinna and Wiman-Valiron on the growth of the meromorphic solutions gives predictions and bounds, but it is not constructive and restricted to meromorphic solutions. The Painlevé approach via the a pri...

We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent equations describing uniformly rotating complex order parameters, both for single-branch (one possible state of locked oscillators) and multi-branch (two possible ...