Studies On Spatiotemporal Chaos Control

Spatiotemporal chaos (STC) and turbulence can occur extensively in a variety of nonlinear dynamical systems with spatial extension, such as cardiac tissue , hydro-dynamical systems , magnetized plasma , reaction-diffusion Systems , and optical systems . In many practical situations such behaviors are considered to be harmful. For instance, a strong tornado can do great damage to human beings; fibrillation in the ventricular myocardium causes fatal cardiac diseases. Because of the potential applications, controlling STC in these systems has attracted much attention of scientists and technologists in the past decade.Flow turbulence and turbulence in fluid and magnetized plasma can be considered to be a type of high-dimensional spatiotemporal chaos. It is generally believed that the control of flow turbulence could benefit from those strategies developed in controlling high-dimensional chaotic systems. Up to the present, spatiotemporal chaos have been investigated extensively. However, controlling flow turbulence based on the understandings of nonlinear dynamics and chaos control is just at the very start. Recently, the global and local pinning control methods developed in spatiotemporal chaos control have been applied to control 2D turbulence described by incompressible Navier-Stokes equations. It is shown that the turbulence can be controlled to desirable time-varying target states. In order to improve the control efficiency, i.e., to achieve successful control as fast as possible with as few as possible number of controllers, Guoning Tang et al have proposed some control strategies to control flow turbulence, such as moving controllers and sporadic feedback control. Some better results have been achieved. However, these methods have some difficulty more or less in practical applications. Therefore, it is interesting to find more practical methods to suppress 2D turbulence for different requirement.In this paper, we study turbulence and spatiotemporal chaos control, focusing on the problems of control efficiency, optimization of flow turbulence control, and the suppression of drift-wave STC in magnetic confinements systems. We suggest some new methods for controlling turbulence and obtain some interesting results. The physical mechanisms underlying those control schemes are heuristically analyzed.In chapter 1, the basic chaotic phenomena, chaos control methods, flow turbulence and drift-wave turbulence are briefly introduced. In Chapter 2, We reported the control of flow turbulence governed by the two-dimensional Navier-Stokes equations. Control is achieved by using mode selective control technique which sporadically filters some modes with small wave numbers out of control signal. The numerical results show that this control strategy can significantly improve control efficiency when control parameters are suitably chosen. The physical mechanism of the control scheme is heuristically analyzed, based on mode-mode interactions.In Chapter 3, Suppression of spatiotemporal chaos in a one-dimensional nonlinear drift-wave equation driven by a sinusoidal wave is considered. Using a constant electric potential signal we demonstrate numerically that the spatiotemporal chaos can be effectively suppressed if the control parameters are properly chosen. The threshold and the controllable range of the control parameters are given. By establishing the kinetic equation of the system energy we find theoretically that an additional driving term in the energy equation is produced by the control signal and it leads up to the frequency entrainment which ultimately leads to STC suppression. The physical mechanism of the control method can help us to understand generation of the coherent structure produced by zonal flows in plasmas.In Chapter 4, We investigate the control of spatiotemporal chaos described by one-dimensional nonlinear drift-wave equation based on the flocking algorithms and propose a method of coupled feedback to suppress the spatiotemporal chaos of the drift-wave. By using real agents and virtual agents as our target, we show numerically that the spatiotemporal chaos can be controlled to a regular state if appropriate control strength is chosen. The physical mechanism is analyzed based on the correlation coefficient.At the end of this paper, We take a concise view of some open questions and the development of chaotic control.