Self-Stable Chaos Control of dc-dc Converter

A new concept related to self-stable chaos control is first put forward, and its theoretical basis and realization are presented from the frequency-domain perspective. With a new analogous-circuit realization of this control its applications in the voltage-mode Buck converter is discussed. The harmonic-balance method is applied to determine the control range of the control parameter. The experiment results given in the last part confirm the validity of the proposed control method.     

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.     

Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems

The purpose of this Letter is to show how a border-collision bifurcation in a piecewise-smooth dynamical system can produce a direct transition from a stable equilibrium point to a two-dimensional invariant torus. Considering a system of nonautonomous differential equations describing the behavior of a power electronic DC/DC converter, we first determine the chart of dynamical modes and show that there is a region of parameter space in which the system has a single stable equilibrium point. Under variation of the parameters, this equilibrium may collide with a discontinuity boundary between two smooth regions in phase space. When this happens, one can observe a number of different bifurcation scenarios. One scenario is the continuous transformation of the stable equilibrium into a stable period-1 cycle. Another is the transformation of the stable equilibrium into an unstable period-1 cycle with complex conjugate multipliers, and the associated formation of a two-dimensional (ergodic or resonant) torus.     

Equilibrium-torus bifurcation in nonsmooth systems

Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium point. We obtain the chart of dynamic modes and show that there is a region of parameter space in which the system has a single stable node equilibrium point. Under variation of the parameters, this equilibrium may disappear as it collides with a discontinuity boundary between two smooth regions in the phase space. The disappearance of the equilibrium point is accompanied by the soft appearance of an unstable focus period-1 orbit surrounded by a resonant or ergodic torus.Detailed numerical calculations are supported by a theoretical investigation of the normal form map that represents the piecewise linear approximation to our system in the neighbourhood of the border. We determine the functional relationships between the parameters of the normal form map and the actual system and illustrate how the normal form theory can predict the bifurcation behaviour along the border-collision equilibrium-torus bifurcation curve.     

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.     

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.     

Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems

We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system.     

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.     

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.     

Non-Smooth Bifurcation and Chaos in a DC-DC Buck Converter

A direct-current-direct-current （DC-DC） buck converter with integrated load current feedback is studied with three kinds of Poincaré maps. The external corner-collision bifurcation occurs when the crossing number per period varies, and the internal corner-collision bifurcations occur along with period-doubling and period-tripling bifurcations in this model. The multi-band chaos roots in external corner-collision bifurcation and often grows into 1-band chaos. A new kind of chaotic sliding orbits, which is more complex for non-smooth systems, is also found in this model.     

Chaos Synchronization Criterion and Its Optimizations for a Nonlinear Transducer System via Linear State Error Feedback Control

Global chaos synchronization of two identical nonlinear transducer systems is investigated via linear state error feedback control. The sufficient criterion for global chaos synchronization is derived firstly by the Gerschgorin disc theorem and the stability theory of linear time-varied systems. Then this sufficient criterion is further optimized in the sense of reducing the lower bounds of the coupling coefficients with two methods, one based on Gerschgorin disc theorem itself and the other based on Lyapunov direct method. Finally, two optimized criteria are compared theoretically.     

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.     

Control Chaos in Hindmarsh--Rose Neuron by Using Intermittent Feedback with One Variable

The mechanism of the famous phase compression is discussed, and it is used to control the chaos in the Hindmarsh-Rose （H-R） model. It is numerically confirmed that the phase compression scheme can be understood as one kind of intermittent feedback scheme, which requires appropriate thresholds and feedback coeffcient, and the intermittent feedback can be realized with the Heaviside function. In the case of control chaos, the output variable （usually the voltage or the membrane potential of the neuron） is sampled and compared with the external standard signal of the electric electrode. The error between the sampled variable and the external standard signal of the electrode is input into the system only when the sampled variable surpasses the selected thresholds. The numerical simulation results confirm that the chaotic H-R system can be controlled to reach arbitrary n-periodical （n = 1, 2, 3, 4, 5, 6,...） orbit or stable state even when just one variable is feed backed into the system intermittently. The chaotic Chua circuit is also investigated to check its model independence and effectiveness of the schemes and the equivalence of the two schemes are confirmed again.     

Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system

The stability conditions in fractional order hyperchaotic systems are derived. These conditions are applied to a novel fractional order hyperchaotic system. The proposed system is also shown to exhibit hyperchaos for orders less than 4. Based on the Routh-Hurwitz conditions, the conditions for controlling hyperchaos via feedback control are also obtained. A specific condition for controlling only fractional order hyperchaotic systems is achieved. Numerical simulations are used to verify the theoretical analysis.     

Synchronization Scheme for Uncertain Chaotic Systems via RBF Neural Network

A sliding mode adaptive synchronization controller is presented with a neural network of radial basis function （RBF） for two chaotic systems. The uncertainty of the synchronization error system is approximated by the RBF neural network. The synchronization controller is given based on the output of the RBF neural network. The proposed controller can make the synchronization error convergent to zero in 5s and can overcome disruption of the uncertainty of the system and the exterior disturbance. Finally, an example is given to illustrate the effectiveness of the proposed synchronization control method.     

Impulsive Control for Fractional-Order Chaotic Systems

We propose an impulsive control scheme for fractional-order chaotic systems. Based on the Takagi-Sugeno （T-S） fuzzy model and linear matrix inequalities （LMfs）, some sufficient conditions are given to stabilize the fractional-order chaotic system via impulsive control. Numerical simulation shows the effectiveness of this approach.     

Comparison of feedback control methods for a hyperchaotic Lorenz system

More and more attention has been payed to the hyperchaotic system for the huge potential applications of hyperchaotic system such as secure communication and more complex structure than chaotic system. So at present the controlling of the hyperchaotic system simply and effectively is a frontier topic of nonlinear science. In this Letter, for the latest hyperchaotic Lorenz system, four feedback control methods were studied with analytic solution and necessary numerical simulations. It is found that the enhancing feedback control approach is the best choice of the given four feedback control methods for its relatively simple external inputs and relatively small necessary feedback coefficient after comparison. The conclusion is a helpful for the choice of control methods of any other chaotic and hyperchaotic systems.     

Torus destruction via global bifurcations in a piecewise-smooth, continuous map with square-root nonlinearity

It has been shown recently that torus formation in piecewise-smooth maps can occur through a special type of border collision bifurcation in which a pair of complex conjugate Floquet multipliers “jump” from the inside to the outside of the unit circle. It has also been shown that a large class of impacting mechanical systems yield piecewise-smooth maps with square-root singularity. In this Letter we investigate the dynamics of a two-dimensional piecewise-smooth map with square-root type nonlinearity, and describe two new routes to chaos through the destruction of two-frequency torus. In the first scenario, we identify the transition to chaos through the destruction of a loop torus via homoclinic bifurcation. In the other scenario, a change of structure in the torus occurs via heteroclinic saddle connections. Further parameter changes lead to a homoclinic bifurcation resulting in the creation of a chaotic attractor. However, this scenario is much more complex, with the appearance of a sequence of heteroclinic and homoclinic bifurcations.     

Controlling Chaos Probability of a Bose-Einstein Condensate in a Weak Optical Superlattice

The spatial chaos probability of a Bose-Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial. chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentaJly.     

Chaotic Dynamics of a Periodically Modulated Josephson Junction

We study the chaotic dynamics of a periodically modulated Josephson junction with damping. The general solution of the first-order perturbed equation is constructed by using the direct perturbation technique. It is theoretically found that the boundedness conditions of the general solution contain the Melnikov chaotic criterion. When the perturbation conditions cannot be satisfied, numerical simulations demonstrate that the system can step into chaos through a period doubling route with the increase of the amplitude of the modulating term. Regulating specific parameters can effectively suppress the chaos.