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.     

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.     

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.     

Phase Space Compression in One-Dimensional Complex Ginzburg-Landau Equation

The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.     

Eliminating spiral waves and spatiotemporal chaos using feedback signal

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this letter we present a feedback scheme to eliminate them. We first collect feedback signals at a certain time t₀. Then wait for the system at the excitable position to enter the recovering state. When the time comes, the feedback signals are added. This scheme has two advantages. Firstly, the tip can be eliminated together with the body of spiral wave. Secondly, the injected feedback signals can be very weak and the duration can be very short so that the original system is nearly not to be affected, which is important for practical applications.     

Frontward-response control of sudden occurrence of chaos

In this Letter, a novel approach to controlling chaos in one-dimensional discrete-time nonlinear autonomous systems is proposed. The method is validated for sudden occurrence of chaos (SOC); its efficacy is demonstrated via numerical simulations of the mappings. The method is simple in implementation. The approach looks highly promising and may have diverse applications.     

Prediction based chaos control via a new neural network

In this Letter, a new chaos control scheme based on chaos prediction is proposed. To perform chaos prediction, a new neural network architecture for complex nonlinear approximation is proposed. And the difficulty in building and training the neural network is also reduced. Simulation results of Logistic map and Lorenz system show the effectiveness of the proposed chaos control scheme and the proposed neural network.     

A Novel Adaptive Observer-Based Control Scheme for Synchronization and Suppression of a Class of Uncertain Chaotic Systems

A novel adaptive observer-based control scheme is presented for synchronization and suppression of a class of uncertain chaotic system. First, an adaptive observer based on an orthogonal neural network is designed. Subsequently, the sliding mode controllers via the proposed adaptive observer are proposed for synchronization and suppression of the uncertain chaotic systems. Theoretical analysis and numerical simulation show the effectiveness of the proposed scheme.     

Filter based non-invasive control of chaos in Buck converter

A non-invasive method for controlling chaos in the voltage-mode Buck converter is proposed by using a hybrid active filter based feedback controller in this Letter. The harmonic balance method is applied to obtaining the bifurcation-point equations of the controlled system. Hence, a stability-boundary diagram is constructed, through which the control parameters are chosen correctly. The results of simulation and experiment are given after all.     

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.     

Hamiltonian description of dipoles on the plane and sphere

Poisson bracket for dipoles of ideal 2D hydrodynamics reduces to Zakharov-Faddeev-Gardner bracket by introducing new variables: coordinates of the vorticity extrema and geodesical distances from the poles to the vorticity lines. The new Hamiltonian equations include the well-known two point-vortex system and a decoupled pair of monopoles as asymptotical cases.     

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.     

Adaptive chaos control and synchronization in only locally Lipschitz systems

In the existing results on chaos control and synchronization based on the adaptive controlling technique (ACT), a uniform Lipschitz condition on a given dynamical system is always assumed in advance. However, without this uniform Lipschitz condition, the ACT might be failed in both theoretical analysis and in numerical experiment. This Letter shows how to utilize the ACT to get a rigorous control for the system which is not uniformly Lipschitz but only locally Lipschitz, and even for the system which has unbounded trajectories. In fact, the ACT is proved to possess some limitation, which is actually induced by the nonlinear degree of the original system. Consequently, a piecewise ACT is proposed so as to improve the performance of the existing techniques.     

Suppression of Chaos in a Bose-Einstein Condensate Loaded into a Moving Optical Superlattice Potential

We have shown that the application of modulating the secondary lattice is an efficient route to suppressing the generation of chaotic traveling waves of a Bose-Einstein Condensate with attractive interatomic interaction loaded into a moving optical superlattiee consisting of two lattices. With the Melnikov method, we obtain the optimal value of the relative phase between the two lattice harmonics for the control of chaos. We also find that the regularization route as the potential depth of the secondary lattice is varied and fairly rich, including the period-doubling bifurcations.     

Parallel velocity shear driven electrostatic waves in a very dense nonuniform magnetoplasma

It is shown that the parallel (magnetic field-aligned) velocity shear can drive the low-frequency (in comparison with the ion gyrofrequency) electrostatic (LF-ES) waves in an ultracold super-dense nonuniform magnetoplasma. By using an electron density response arising from the balance between the electrostatic and quantum Bohm forces, as well as the ion density response deduced from the continuity and momentum equations, a wave equation for the LF-ES waves is derived. In the local approximation, a new dispersion relation is obtained by Fourier transforming the wave equation. The dispersion relation reveals an oscillatory instability of dispersive drift-like modes in super-dense quantum magnetoplasmas.     

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.     

Suppression of Spiral Waves by Voltage Clamp Techniques in a Conductance-Based Cardiac Tissue Model

A new control method is proposed to control the spatio-temporal dynamics in excitable media, which is described by the Morris–Lecar cells model. It is confirmed that successful suppression of spiral waves can be obtained by spatially clamping the membrane voltage of the excitable cells. The low voltage clamping induces breakup of spiral waves and the fragments are soon absorbed by low voltage obstacles, whereas the high voltage clamping generates travel waves that annihilate spiral waves through collision with them. However, each method has its shortcomings. Furthermore, a two-step method that combines both low and high voltage clamp techniques is then presented as a possible way of out this predicament.     

Impulsive control of a class of vibro-impact systems

In this Letter, the impulsive control method is developed to stabilize the chaotic motions in a class of vibro-impact systems. The strategy of the control is to implement the pulses just when the impact occurs. As applications of this method, we present the numerical simulations of two impact oscillators. Our numerical results indicate that the method used here could suppress chaos into periodic orbits which embedded in the chaotic attractor effectively, and also show that the method is robust even for high levels of multiplicative noise or additive noise.     

Preserving synchronization under matrix product modifications

In this article we present a methodology under which stability and synchronization of a dynamical master/slave system configuration are preserved under modification through matrix multiplication. The objective is to show that under a defined multiplicative group, hyperbolic critical points are preserved along the stable and unstable manifolds. The properties of this multiplicative group were determined through the use of simultaneous Jordan decomposition. It is also shown that a consequence of this approach is the preservation of the signature of the Jacobian matrix associated with the dynamical system. To illustrate the results we present several examples of different modified systems.     

Adaptive Functional Projective Lag Synchronization of a Hyperchaotic Rössler System

We explain the functional projective lag synchronization of a hyperchaotic Rössler system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. Based on Lyapunov stability theory, an active control method and adaptive control law are employed to make the states of two hyperchaotic Rössler systems asymptotically synchronized. Finally, some numerical examples are provided to show the effectiveness of our results.