Controlling Flow Turbulence Using Local Pinning Feedback

Flow turbulence control in two-dimensional Navier-Stokes equation is considered. By applying local pinning control only to a single component of flow velocity field, the flow turbulence can be controlled to desirable targets. It is found that with certain number of controllers there exist an optimal control strength at which control error takes minimum value, and larger and smaller control strengths give worse control efficiency. The physical mechanism underlying these strange control results is analysed based on the interactions between different types of modes.     

Controlling Spatiotemporal Chaos with a Generalized Feedback Method

The usual linear variable feedback control method is extended to a generalized function feedback scheme. The scheme is applied to high-dimensional spatiotemporal systems. By a combination of local generlized feedback control and the spatial coupling effect among elements, turbulent motion can be successfully eliminated.     

Suppression of spatiotemporal chaos under a constant electric potential signal

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 can lead up to the frequency entrainment. Moreover, when the regular state is reached under the control, the system energy oscillates quasi-periodically, while the additional driving term decays to zero.     

Hexagonal Standing-Wave Patterns in Periodically Forced Reaction-Diffusion Systems

The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.     

Resonance in Defect Turbulence under Periodic External Force

The periodically forced spatially extended Brusselator is investigated in the chaotic regime. We explore resonant or non-resonant patterns generated under various forcing frequencies and forcing amplitudes. Resonant spatially uniform oscillation and irregular structures are found. Furthermore two types of regular spatial patterns are generated under appropriate parameters. Our results of numerical simulations demonstrate that periodic force can give rise to resonant patterns in forced systems of spatiotemporal chaos similar to the situation of forced systems of regular oscillations.     

Additive Temporal Coloured Noise Induced Eckhaus Instability in Complex Ginzburg-Landau Equation System

The effect of additive coloured noises, which are correlated in time, on one-dimensional travelling waves in the complex Ginzburg-Landau equation is studied by numerical simulations. We found that a small coloured noise with temporal correlation could considerably influence the stability of one-dimensional wave trains. There exists an optimal temporal correlation of noise where travelling waves are the most vulnerable. To elucidate the phenomena, we statistically calculated the convective velocities Vg of the wave packets, and found that the coloured noise with an appropriate temporal correlation can decrease Vg, making the system convectively more unstable.     

Dynamics of Vortex-Wave under a Travelling-Wave Modulation

The mechanism of destabilization is studied for the rotating vortices （scroll waves and spiral waves） in excitable media induced by a parameter modulation in the form of a travelling-wave. It is found that a rigid rotating spiral in the two-dimensional （2D） system undergoes a synchronized drift along a straight line, and a 3D scroll ring with its filament closed into a circle can be reoriented only if the direction of wave number of a travelling-wave perturbation is parallel to the ring plane. Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scroll ring, the approximate formulas are given to exhibit qualitative agreements with the observed results.     

Self-Organization in Coupled Map Scale-Free Networks

We study the self-organization of phase synchronization in coupled map scale-free networks with chaotic logistic map at each node and find that a variety of ordered spatiotemporal patterns emerge spontaneously in a regime of coupling strength. These ordered behaviours will change with the increase of the average finks and are robust to both the system size and parameter mismatch. A heuristic theory is given to explain the mechanism of self-organization and to figure out the regime of coupling for the ordered spatiotemporal patterns.     

Controlling Spiral Dynamics in Excitable Media by a Weakly Localized Pacing

Spiral dynamics controlled by a weakly localized pacing around the spiral tip is investigated. Numerical simulations show two distinct characteristics when the pacing is applied with the weak amplitude for suitable frequencies： for a rigidly .rotating spiral, a transition from rigid rotation to meandering motion is observed, and for unstable spiral waves, spiral breakup can be prevented. Successfully preventing spiral breakup is relevant to the modulation of the tip trajectory induced by a localized pacing.     

Synchronization defect lines in complex-oscillatory target waves

It is well known that one of key features of spiral waves in complex-oscillatory media is the appearance of synchronization defect lines, across which the phase of the oscillation changes by multiplies of 2π. In this Letter, we report the appearance of synchronization defect lines in target waves in complex-oscillatory media by studying a model of two-dimensional Rössler reaction-diffusion system subject to an appropriate periodic force in a small region of the center of domain. The geometric structure and stability of the defect lines are studied.     

Intermittency Growth in Fluid Turbulence

Measurement and phenomenological analyses of intermittency growth in an experimental turbulent pipe flow and numerical turbulence are performed, for which working definitions such as degree, increment, and growth rate of intermittency are introduced with the help of quasiscaling theory. The logarithmic-normal inertial scaling model is extended to quasiscaling as the second-order truncation of the Taylor expansion and is used for studying the intermittency growth problem. The extended self-similarity properties are shown to be not consistent with the monotonicity of the third order local quasiscaling exponent and the nonmonotonic behaviour of the intermittency growth rate as a result of bottleneck. Digestions of the results with scale-dependent multifractals are provided.     

The boundary-induced spiral wave drift in the complex Ginzburg–Landau equation

We numerically investigate the boundary-induced spiral wave drift in the complex Ginzburg–Landau equation. We find some novel phenomena for the spiral drifting dynamics such as the chaotic behaviors, the transient chaos and asymmetrical attractors.     

Wave Grouping of a Drifting Spiral Wave in the Presence of an External Field

The phenomenon of wave grouping, in which the dense waves and the sparse waves can form groups in front of the spiral tip when the spiral wave is meandering, has been reported in a chemical reaction system recently. We present a method to realize the phenomenon of wave grouping by applying an external field to the system. The numerical simulations are carried out on the basis of the FitzHugh-Nagumo equations.     

Kinematic model of propagating arc-like segments with feedback

Using a kinematic approach, we propose a model of arc-like wave segments in which the free ends are stabilized by using a feedback algorithm. The model can demonstrate the experimental results and numerical computations of a reaction-diffusion system. This model also reveals some aspects of spiral wave dynamics with the free ends including not only the stabilization of wave segments using feedback, but also a critical behavior with respect to the initial wave size in media with fixed excitability.     

Spatiotemporal chaos control in two-wave driven systems

Spatiotemporal chaos control is considered by taking a one-dimensional driven/damped nonlinear drift-wave equation as a model. We apply an additional sinusoidal wave to suppress spatiotemporal chaos, and the system becomes a two-sinusoidal-wave driven system (the original driving wave with frequency ω and an additional controlling wave with frequency Ω). Numerical simulations show that when the frequency of the controlling wave is in the proper range, spatiotemporal chaos can be modified into a regular state where the amplitudes of all modes vary periodically with frequency Ω-ω while the phases of all modes evolve quasi-periodically with a running frequency Ω overlapped by a small modulation of frequency Ω-ω. The physical reason for this peculiar phenomenon is attributed to a frequency entrainment in the competition of the two external waves.     

Effects of Periodic Forcing Amplitude on the Spiral Wave Resonance Drift

We study dynamics of spiral waves under a uniform periodic temporal forcing in an excitable medium. With a specific combination of frequency and amplitude of the external periodic forcing, a resonance drift of a spiral wave occurs along a straight line, and it is accompanied by a complicated ‘flower-like＇ motion on each side of this bifurcate boundary line. It is confirmed that the straight-line drift frequency of spiral waves is not locked to the nature rotation frequency as the forcing amplitude expends are further verified numerically for a simplified kinematical the range of the spiral wave frequency. These results model.     

Turbulent Boundary Layer Control via a Streamwise Travelling Wave Induced by an External Force

Turbulent boundary layer control via a streamwise travelling wave is investigated based on direct numerical simulation of an incompressible turbulent channel flow. The streamwise travelling wave is induced on one side wall of the channel by a spanwise external force, e.g., Lorenz force, which is con~ned in the viscous sublayer. As the control strategy used in this study has never been examined, we pay our attention to its efficiency of drag control. It is revealed that the propagating direction of the travelling wave, i.e., the downstream or upstream propagating direction with respect to the streamwise flow, has an important role on the drag control, leading to a significant drag reduction or enhancement for the parameters considered. The coherent structures of turbulent boundary layer are altered and the underlying mechanisms are analysed. The results obtained provide physical insight into the understanding of turbulent boundary layer control.     

Fuzzy Impulsive Control of Permanent Magnet Synchronous Motors

The permanent magnet synchronous motors （PMSMs） may experience chaotic behaviours with systemic parameters falling into a certain area or under certain working conditions, which threaten the secure and stable operation of motor-driven. Hence, it is important to study the methods of controlling or suppressing chaos in PMSMs. In this work, the Takagi-Sugeno （T-S） fuzzy impulsive control model for PMSMs is established via the T-S modelling methodology and impulsive technology. Based on the new model, the control conditions of asymptotieal stability and exponential stability for PMSMs have been derived by the Lyapunov method. Finaily, an illustrated example is also given to show the effectiveness of the obtained results.     

Tracking Desired Trajectory in a Vibro-Impact System Using Backstepping Design

Based on the backstepping design of smooth systems, we developed a new control law to achieve chaos control for a vibro-impact system. In our control strategy, a novel and effective controller is designed such that the output of the vibro-impact system can track any desired trajectory in its domain. The single-degree-of-freedom vibro-impact system is taken as an example to show this control procedure. Numerical simulations are provided to verify the effectiveness of the proposed method.     

Preservation of stability and synchronization in nonlinear systems

Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results.