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.

中文翻译：

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当局部耦合的混沌振荡器网格全局耦合到另一个混沌振荡器时，从混沌同步过渡到极限周期振荡

一些具有相互作用的混沌子单元的物理系统在同步时会表现出从混沌到间歇循环的动态过渡，例如由于湍流中各个子系统之间的反馈而引起的振荡不稳定性，这是通过间歇性实现的。我们描述了当混沌振荡器的网格与不同的混沌振荡器扩散耦合时，通过间歇性从混沌到极限循环振荡的过渡。为了达到这个目的，我们证明了这种转变的出现，以限制与混沌Van der Pol振荡器双向耦合的局部耦合的不相同的Rssler振荡器的网格中的周期振荡。进一步，我们报告了在从不同步的混沌过渡到同步的周期的过程中，存在对称破坏现象，例如嵌合体状态和孤立状态。我们还确定了这种时间路线，该同步路线是通过间歇性相位同步，然后是混沌同步和相位同步，从去同步混沌到广义同步的过渡。此外，我们报告了在混沌范德波尔振荡器的时间序列和Rössler系统的平均场时间序列中多重分形的损失和无标度行为的损失。在热声，气动弹性和气动声学系统中出现振荡不稳定性的过程中已观察到这种行为。