| Contents |
| A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that the solutions possess different characteristics, depending on the section of the boundary of the SR where they appear. We study the birth of these solutions and how they evolve when the coupling strength increases, and determine the diagram of solutions in phase space. We also 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. |
|