Property change of unstable fixed point and phase synchronization in controlling spatiotemporal chaos by a periodic signal.

Mechanisms for the suppression of spatiotemporal chaos (STC) in one-dimensional driven drift-wave system to a spatially regular state by a periodic signal are investigated. In the driving wave coordinate, by transforming the system to a set of coupled oscillators (modes) moving in a periodic potential, it is found that the modes can be enslaved one by one through phase synchronization (PS) by the control signal; for some modes frequency-locking occurs while the other modes display multilooping PS without frequency-locking. Further study of the linear behavior of the modes shows that the saddle point embedded in the STC is changed to an unstable focus, which makes it possible for the imperfect PS to change to a perfect functional one, leading to the suppression of the STC.

Controlling drift-wave turbulence using time-delay and space-shift autosynchronization feedback.

Drift-wave turbulence control in a one-dimensional nonlinear drift-wave equation driven by a sinusoidal wave is considered. We apply time-delay and space-shift feedback signals, to suppress turbulence. By using global and local pinning strategies, we show numerically that the turbulent state can be controlled to periodic states effectively if appropriate time-delay length and space-shift distance are chosen. The physical mechanism of the control scheme is understood based on the energy-minimum principle.

Riddling of the orbit in a high dimensional torus and intermittent energy bursts in a nonlinear wave system.

The bifurcation scenario in a practically interesting nonlinear wave system is investigated by using a new scheme that is performed in a purely nonlinear wave framework with the Doppler effect taken into account. High-dimensional tori with three or four competing frequencies are observed. With variation of parameters a riddling of the orbit may occur intermittently due to tangency in certain dimensions, which temporarily spoils the toroidal topology and induces an energy burst where spatial coherence of the wave is lost.

Critical dynamic events at the crisis of transition to spatiotemporal chaos.

In the driven/damped drift-wave plasma system a collision of the weak chaotic attractor with a saddle point is demonstrated at the crisis that induces a transition from a spatially coherent state to spatiotemporal chaos (STC). The phenomenon of the collision is consistent with the previous observation of the "pattern resonance" that triggers the crisis. Subsequent to the collision, before the system is ejected to the STC attractor, there is evidence of another critical dynamic event involving state transition of a mode phase. The second event plays a crucial role in the destruction of the spatial coherence.

On-off collective imperfect phase synchronization and bursts in wave energy in a turbulent state.

A new type of synchronization, on-off collective imperfect phase synchronization, is found in a turbulent state. In the driver frame the nonlinear wave system can be transformed to a set of coupled oscillators moving in a potential related to the unstable steady wave. In "on" stages the oscillators in different spatial scales adjust themselves to collective imperfect phase synchronization, inducing strong bursts in the wave energy. The interspike intervals display a power-law distribution. In addition to the embedded saddle point, it is emphasized that the delocalization of the master mode also plays an important role in developing the on-off synchronization.