Phase synchronization in coupled chaotic oscillators with time delay

Explosive synchronization in a turbulent reactive flow system

The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely, a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.

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

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.

TIME DELAY MODEL OF RNA SILENCING

RNA silencing (also known as RNA interference) suppresses the expression of genes posttranscriptionally. We propose a time delay model of RNA silencing through a system consisting of double-stranded RNA (dsRNA), RNA-induced silencing complex (RISC), messenger RNA (mRNA), and RISC–mRNA complex. The time delay model is based on the consideration that the regeneration (or degradation) of the RISC–mRNA complex needs a finite time τ. The model equations are analyzed using nonlinear dynamics methods, in particular the Hopf bifurcation theorem, and they are solved numerically. From the accomplished analytical and numerical calculations, it becomes clear that time delay τ is a key factor in the behavior of the model. In this case, it has a destabilizing effect on the silencing process.