Controlling chaos by a delayed continuous feedback in a gas discharge plasma

Control of chaos by a delayed continuous feedback is studied experimentally in a gas discharge plasma. The power spectrum, the maximum of Lyapunov exponents and the time series of the signals all indicate that the period-1 unstable periodic orbit is controlled successfully. The dependence of the control on the delay time and the feedback gain as well as the strength of white noise is also investigated in detail. The experimental results show that the scaling index of the control versus the strength of white noise is 1.995, which is very close to that obtained from the simple logistic map.     

A perturbation method to the tent map based on Lyapunov exponent and its application

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation.     

Research on the chaos recognition method based on differential entropy

Phase space reconstruction is the first step to recognizing the chaos from observed time series. On the basis of differential entropy, this paper introduces an efficient method to estimate the embedding dimension and the time delay simultaneously. The differential entropy is used to characterize the disorder degree of the reconstructed attractor. The minimum value of the differential entropy corresponds to the optimum set of the reconstructed parameters. Simulated experiments show that the original phase space can be effectively reconstructed from time series, and the accuracy of the invariants in phase space reconstruction is greatly improved. It provides a new method for the identification of chaotic signals from time series.     

Bubble nonlinear dynamics and stimulated scattering process

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller–Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition.     

Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

The three most widely used methods for reconstructing the underlying time series via the recurrence plots (RPs) of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.     

Simulated Melting Curve of NaC1 up to 200 kbar

The melting curve of NaCI is studied up to 200 kbar by means of the shell-model molecular dynamics method, usiug massive shell core interaction potentials. The model for the interatomic interaction is shown to produce reasonable results at a wide range of pressures in bulk transitions. The pressure dependence of the melting curve of NaCl was calculated and the result was modified on the assumption of overheating due to the small system size and small time scale simulation. The final result is in good agreement with the corrected experimental values, accounting for melting mechanisms such as surface heating or superheating. Therefore, it is believed that bulk transition simulation at constant pressure indeed provides a useful tool for studying the melting transition.     

Optical Erasure Characteristics of Holograms in Batch Thermal-Fixing

The optical erasure dynamics in a batch-thermal fixing scheme of holographic storage in photorefractive crystals is investigated theoretically and experimentally. The inter-batch optical erasure time constant τF is introduced to specify the optical erasure to compensated gratings, and measured in a sophisticated experiment. The experimental result shows that τF is much longer than the intra-batch optical erasure time constant τE. The difference between τFand τE is fundamental for enhancing nonvolatile storage density.     

Decoherence of a Double Quantum Dot Charge Qubit Approached with Redfield Equation

In this paper, we investigate the decoherence time of a double quantum dot （DQD） charge qubit in three kinds of baths through solving dynamics of the qubit. The dynamics of the qubit is investigated with Redfield master equation. It is shown that the decoherence time of the qubit in Ohmic bath has the same order of magnitude as the experiments reported. When the environment is modeled with the supra-Ohmic bath the decoherence time of the qubit is shorter than the experimental result. And when modeled with the sub-Ohmic bath the decoherence time of the qubit is longer than the experimental result.     

Control of chaos in Frenkel–Kontorova model using reinforcement learning

It is shown that we can control spatiotemporal chaos in the Frenkel–Kontorova(FK) model by a model-free control method based on reinforcement learning. The method uses Q-learning to find optimal control strategies based on the reward feedback from the environment that maximizes its performance. The optimal control strategies are recorded in a Q-table and then employed to implement controllers. The advantage of the method is that it does not require an explicit knowledge of the system, target states, and unstable periodic orbits. All that we need is the parameters that we are trying to control and an unknown simulation model that represents the interactive environment. To control the FK model, we employ the perturbation policy on two different kinds of parameters, i.e., the pendulum lengths and the phase angles. We show that both of the two perturbation techniques, i.e., changing the lengths and changing their phase angles, can suppress chaos in the system and make it create the periodic patterns. The form of patterns depends on the initial values of the angular displacements and velocities. In particular, we show that the pinning control strategy, which only changes a small number of lengths or phase angles, can be put into effect.     

Time Series Prediction Based on Chaotic Attractor

A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.     

Continuous feedback control of KdV Burgers system

The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationary points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment separately.     

Formation of Singularities in One—Dimensional Hydromagnetic Flow

Two results on the formation of singularities in solutions to the system of one-dimensional hydromagnetic dynamics are presented.In particular,it is shown that shocks form from a smooth spatial periodic flow in a finite time if the initial amounts of entropy and the “magnetic field” in each period are smaller than those of sound waves.A quantitative estimate of blow-up time is also given.     

Control of firing activities in thermosensitive neuron by activating excitatory autapse

Temperature has distinct influence on the activation of ion channels and the excitability of neurons, and careful change in temperature can induce possible mode transition in the neural activities. The formation and development of autapse connection to neuron can enhance its self-adaption to external stimulus, and thus the firing patterns in neuron can be controlled effectively. The autapse is activated to drive a thermosensitive neuron, which is developed from the FitzHugh–Nagumo neural circuit by incorporating a thermistor, and the dynamics in the neural activities is explored to find mode dependence on the temperature and autaptic current. It is found that the firing modes can be controlled by temperature, and the neuron is wakened from resting state to periodic oscillation with the increase of temperature. Furthermore, the intensity and the intrinsic time delay in the autapse are respectively adjusted to control the neural activities, and it is confirmed that appropriate setting for autaptic current can balance and enhance the temperature effect on the neural activities.     

Phase Space Prediction Model Based on the Chaotic Attractor

A new prediction technique is proposed for chaotic time series.The usefulness of the technique is that it removes some false neighbouring points which are not suitable for the local estimation of the dynamics systems.We use a feedforward neural network to approximate the local dominant Lyapunov exponent,and choose the neighbouring points by the exponent.The model is tested for the convection amplitude of the Lorenz model,and the results indicate that this prediction technique can improve the prediction of chaotic time series.     

Existence of horseshoe maps in voltage-mode controlled buck converters

In this paper, chaos in a voltage-mode controlled buck converter is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behaviour. The essential tool is the horseshoe hypotheses proposed by Kennedy and Yorke, which will be reviewed prior to the discussion of the main finding.     

FAST EVOLVING MULTI-LAYER PERCEPTRONS FOR NOISY CHAOTIC TIME SERIES MODELING AND PREDICTIONS

A fast evolutionary programming (FEP) is proposed to train multi-layer perceptrons (MLP) for noisy chaotic time series modeling and predictions. This FEP, which uses a Cauchy mutation operator that results in a significantly faster convergence to the optimal solution, can help MLP to escape from local minima. A comparison against back-propagation-trained networks was performed. Numerical experimental results show that the FEP can help MLP better capturing dynamics from noisy chaotic time series than the back-propagation algorithm and produce a more consistently modeling and prediction.     

Controlling Chaos in Hénon Map by the Constant Feedback Method

We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise.     

Controlling Chaos in Hénon Map by the Constant Feedback Method

We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise.     

Suppression of decoherence by bath ordering

The dynamics of two coupled spins-1/2 coupled to a spin-bath is studied as an extended model of the Tessieri--Wilkie Hamiltonian. The pair of spins served as an open subsystem is prepared in one of the Bell states and the bath consisting of some spins-1/2 is in a thermal equilibrium state from the very beginning. It is found that with increasing coupling strength of the bath spins, the bath forms a resonant antiferromagnetic order. The polarization correlation between the two spins of the subsystem and the concurrence of it are recovered to some extent in the isolated subsystem. This suppression of the subsystem decoherence may be used to control the quantum devices in practical applications.