Symmetry broken states in an ensemble of globally coupled pendulums

Abstract

We consider the rotational dynamics in an ensemble of identical globally coupled pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of the community elements. There exist the wide variety of inphase and out-of-phase regimes. Many of these states appear due to instability of in-phase rotational mode that leads to partially broken symmetry in the considered model. Our theoretical analysis allows one to find the boundaries of the instability domain for ensembles with arbitrary number of pendulums. In the case of three elements, for system control parameter sets corresponding to the unstable in-phase rotations we numerically find a number of out-of-phase rotation modes and study in detail their stability and bifurcations. We demonstrate that chaotic behavior arises throw the cascade period doubling bifurcations and torus destruction. As a result, we obtain a sufficiently detailed picture of the symmetry breaking and existence of various regular and chaotic states in an ensemble of identical globally coupled pendulums. In particular, we show that the family of symmetry-broken states includes chimera attractors. In these regimes, one part of the oscillators moving irregularly is synchronized, and the other pendulums rotate separately. We directly demonstrate the example of chimera states in the system under discussion for the cases of three and four number of elements.PACS numbers: 05.45.Xt, 45.20.dc

Rotobreathers in a chain of coupled elastic rotators

“…The model of cou-pled rotators [17] found its application in describing the relative rotation of polymer fragments around the axis of the macromolecule [45] and it was shown that a strong effect of thermal rectification is possible in a system of polyethylene nanofibers [46], possibly due to the excitation of rotobreather modes [34]. Appearance of chaos and synchronization structures in the chains of rotating pendulums have been analyzed in the works [35][36][37][38].…”