Synchronization transition from chaos to limit cycle oscillations when a locally coupled chaotic oscillator grid is coupled globally to another chaotic oscillator

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.

Understanding dynamical states observed in a thermo-acoustic system from perspective of frequency-phase relationship derived from a probabilistic oscillator model

“…On the other hand, we illustrate how frequency-phase relationship could result in the observed behavior. In a sense, this follows the deduction on intermittency and other dynamical states [46,31], whereby properties of the observed intermittent behavior is elucidated by a stochastically forced Van-der-Pol oscillator in the former and the mean frequency locking in the latter.…”

“…The assumption is drastic, but is justified on the reason that decoupled oscillators result in oscillations at their own intrinsic frequency leading to stable combustion. Whereas coupled oscillators, with coupling provided through parametric or functional means [31,32,33], result in synchronized behavior. Further, a range of qualitatively similar dynamical states that range from combustion noise to limit cycle oscillations have been reproduced by such models [32,33], thereby providing reliable lower order models for less demanding physical and computational resources.…”

Asymmetry induced suppression of chaos

“…However, we must add the caveat that its full scope and extent is as yet undetermined. So an open question here is the generality of these results under varying dynamics and coupling classes, and this warrants future work across different systems, both theoretical and experimental 42 . Lastly, we would like to discuss these findings from a conceptual point of view.…”

Seeds of phase transition to thermoacoustic instability

“…Such an increase in CC q , especially before any appreciable change in the global measures of p rms and Q rms , indicates an emerging teleconnection between Z1, Z2 and Z3 before the OOD. In a recent study Godavarthi et al (2020) utilized non-identical Rössler oscillators and a chaotic Van der Pol oscillator to represent the spatially resolved heat release rate and the acoustic pressure respectively. They showed that with increase in the coupling strength, the acoustic pressure fluctuations changed from a chaotic state to a periodic state via intermittency.…”