Collective topological dynamics in the Frenkel-Kontorova chains

Topological dynamics of an array of harmonically coupled damped dc-driven nonlinear oscillators are studied by introducing a dynamical contraction factor and a deviation factor. Different dynamical transitions are identified, and topological changes for these transitions are studied. A bifurcation from the kink state to the kink-antikink-pair state is found, which relates the topological change to the spatiotemporal dynamics of the system. The presence of antikinks leads to the extension of the localized kink, and collisions of kinks and antikinks induce strong oscillations of the topology of the array.