Consider any network of n identical Kuramoto oscillators in which each oscillator is coupled bidirectionally with unit strength to at least μ(n−1) other oscillators. There a critical value the connectivity, μc, such that whenever μ>μc, system guaranteed converge all-in-phase synchronous state for almost all initial conditions, but when μ<μc, there are networks stable states. The p...

The dynamics of large systems coupled oscillators is a subject increasing importance with prominent applications in several areas such as physics and biology. Kuramoto model, where set move around circle representing their phases, paradigm this field, exhibiting continuous transition between disordered synchronous motion. Reinterpreting the rotating unit vectors, model was extended to higher di...

We study the global smooth solution for the coupled Kuramoto-Sivanshinsky-KdV system in two-dimensional space. The model is proposed to describe the surface waves on multi-layered liquid films. The global solution is obtained for general initial data, using an a priori estimate for the nonlinear system, and the smoothness of such solution is established in t > 0.

The cellular energy-sensing kinase AMPK is known to be activated in neurons in response to metabolic insults, but the downstream consequences have been unclear. A study by Kuramoto and colleagues in this issue of Neuron favors the idea that AMPK activation is neuroprotective, and suggests a potential mechanism for this effect involving phosphorylation of the GABA(B) receptor.

We consider the periodic initial value problem for the Kuramoto–Sivashinsky (KS) equation. We approximate the solution by discretizing in time by implicit–explicit BDF schemes and in space by a pseudo–spectral method. We present the results of various numerical experiments.