Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model

Details Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model

2011-08-16

arxiv.org/abs/1108.3271v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

14 pages, 13 figures

Scientific paper

In this work we study the local coupled Kuramoto model (LCKM) with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show some unexpected phenomena resulting from the symmetry properties: the existence of local attractors in the synchronized region; stability exchange for crossing fixed points; fixed point stability dependent on the manifold dimension; chaotic period and intermittent phase slips. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic.

Affiliated with

Also associated with

No associations

Rating

Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-196265