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Abstract:
Some physical systems with interacting chaotic subunits, when synchronized, exhibit a dynamical transition from chaos to limit cycle oscillations via intermittency such as during the onset of oscillatory instabilities that occur due to feedback between various subsystems in turbulent flows. We depict such a transition from chaos to limit cycle oscillations via intermittency when a grid of chaotic oscillators is coupled diffusively with a dissimilar chaotic oscillator. Toward this purpose, we demonstrate the occurrence of such a transition to limit cycle oscillations in a grid of locally coupled non-identical Rössler oscillators bidirectionally coupled with a chaotic Van der Pol oscillator. Further, we report the existence of symmetry breaking phenomena such as chimera states and solitary states during this transition from desynchronized chaos to synchronized periodicity. We also identify the temporal route for such a synchronization transition from desynchronized chaos to generalized synchronization via intermittent phase synchronization followed by chaotic synchronization and phase synchronization. Further, we report the loss of multifractality and loss of scale-free behavior in the time series of the chaotic Van der Pol oscillator and the mean field time series of the Rössler system. Such behavior has been observed during the onset of oscillatory instabilities in thermoacoustic, aeroelastic, and aeroacoustic systems. This model can be used to perform inexpensive numerical control experiments to suppress synchronization and thereby to mitigate unwanted oscillations in physical systems.
During the onset of oscillatory instabilities that occur due to feedback between various subsystems in turbulent systems, we observe a transition from chaos to order. Examples for these are the occurrence of oscillatory instabilities in thermoacoustic, aeroelastic, and aeroacoustic systems. The onset of the oscillatory instabilities in such systems is shown as a transition from chaos to limit cycle oscillations via intermittency.1–3 Further, the synchronization framework has been applied to describe the onset of thermoacoustic and aeroelastic instabilities. The onset of thermoacoustic instabilities is described as the occurrence of synchronization between the acoustic field and the global heat release rate in a turbulent combustor.4 The onset of aeroelastic instability in a pitch-plunge aeroelastic system is described as the onset of synchronization between the pitch and the plunge modes.5 Further, a spatiotemporal transition from disorder to order via a chimera-like state is detected.6,7 Such systems with many interacting subunits are generally modeled using a grid of oscillators. However, the transition in the dynamics from chaos to limit cycle oscillations among chaotic oscillators has been observed only with conjugate coupling or time delay coupling. Here, we show that this transition to limit cycle oscillations is also possible when different chaotic oscillators are coupled. We show an alternate route wherein a transition from chaos to limit cycle oscillations occurs when a grid of locally coupled Rössler oscillators is bidirectionally coupled with a chaotic Van der Pol (VDP) oscillator. We explore the temporal and spatiotemporal synchronization route to limit cycle oscillations. We further draw some analogies between the model in our study with the experimental results from thermoacoustic and aeroelastic systems. Models such as ours can be used to perform inexpensive numerical control experiments to suppress the limit cycle oscillations having ruinously large amplitudes observed during the occurrence of oscillatory instabilities in such systems
