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The collective behavior of the ensembles of coupled nonlinear oscillator isone of the most interesting and important problems in modern nonlineardynamics. In this paper, we study rotational dynamics, in particular space-timestructures, in locally coupled identical pendulum-type elements chains thatdescribe the behavior of phase-locked-loop systems, distributed Josephsonjunctions, coupled electrical machines, etc. The control parameters in theconsidered chains are: dissipation, coupling strength, and number of elements.In the system under consideration, the realized modes are synchronous infrequency and synchronous (in-phase) or asynchronous (out-of-phase) in phase.In the low dissipation case, the in-phase synchronous rotational regimeinstability region boundaries are theoretically found and the bifurcationsleading to the loss of its stability are determined. The analysis was carriedout for chains of arbitrary length. The existence of various out-of-phasesynchronous rotational modes types is revealed: completely asynchronous inphases and the cluster in-phase synchronization regime. Regularities oftransitions from one type of out-of-phase synchronous mode to another areestablished. It was found that at certain coupling parameter values, thecoexistence of stable in-phase and out-of-phase synchronous modes is possible.It was found that for arbitrary chain length, the number of possible stableout-of-phase modes is always one less than the chain elements number.Analytical results are confirmed by numerical simulations.

Synchronization structures in the chain of rotating pendulums