We use recurrence analysis udto investigate the forced synchronization of a selfud-udexcited thermoacoustic udsystemud. The system consists of uda udswirlud-udstabilized turbulent premixed flame in audn openud-udendedudduct.udWe udapplyudperiodic acoustic forcingudto this system at uddifferent amplitudes and frequencies around uditsudnatural udselfud-udexcited frequency, and udexamine its responseudvia unsteady pressureudmeasurements. udOn increasing udthe forcing amplitude, we observe twoudbifurcations: udfrom a periodic limit cycle (unforced) to qua-udsipeudriodicudity ud(weak forcing) and then to lockud-udin (strong fudorcing).udTo udanalyseudtheudseudbifurcationsud, we uduseudcrossud-udrecurrence plots (CRPs) udof the udunsteadyudpressure and acoustic forcing.udWe find that the different udtime scales udcharacterizingudthe quasiperiodicudityudand the transition to lockud-udin appear as dudistinct structures udin the CRPsud.udWe then examine those structures udusingudcross udrecurrence quantification analysisud(udCudRQA)udand udfind that theudirudrecurrence udquantities udchange even before the system transitions to lockud-udinud.udThis udshowsudthatudCRPs andudCRQA can be usedudas alternativeudnonlinearudtooludsudto studyudforcedudsynchronizationudin thermoacoustic systems, udcomplementingudclassicaludlinear tools udsuch asudspectral analysis.
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