近代物理学"混沌理论"浅解

"混沌理论"的诞生,解决了现代物理理论研究中有关传统的确定性理论领域中的随机性现象和传统的随机性理论研究的确定性问题。从简单的数学游戏和单摆入手,解说了混沌运动的产生及主要特征,通过介绍"混沌理论"建立的史话,从更新、更简单的角度去理解"混沌理论",为"混沌理论"的普及起到了前导作用。

FLIGHT CONFLICT FO RECASTING BASED ON CHAOTIC TIME SERIES

In order to grasp the evolution of flight conflict amount accurately and to forecast the amount, chaos in flight conflicts is studied. Firstly, a fault tree of flight conflicts is established based on the man-machine-environ- ment system engineering theory. The chaotic characteristics of flight conflict are analyzed from the qualitative point of view. Secondly, an improved chaotic algorithm for the largest Lyapunov exponent is proposed based on the small-data method and the wavelet de-noising theory. Chaos in flight conflict time series is identified by the improved chaotic algorithm from the quantitative point of view. Finally, a case study by the chaos forecasting al- gorithm is performed and the results are evaluated by the gray error checking ： Correlative value of posterior error is 0. 220 9〈0. 35, and micro-error probability is 0. 985 3〉0.95. Such results show the chaos forecasting algo- rithm is effective, thus it is feasible to analyze and forecast flight conflict by chaotic theory.

INTERNET TRAFFIC DATA FLOW FORECAST BY RBF NEURAL NETWORK BASED ON PHASE SPACE RECONSTRUCTION

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated, and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is construct- ed based on radial basis function （RBF） to forecast actual Internet traffic data flow. Simulation results show that, compared with other forecasts of the forward-feedback neural network, the forecast of the RBF neural network based on the chaos theory has faster learning capacity and higher forecasting accuracy.

Research on a non-linear chaotic prediction model for urban traffic flow

In order to solve serious urban transport problems, according to the proved chaotic characteristic of traffic flow, a non linear chaotic model to analyze the time series of traffic flow is proposed. This model reconstructs the time series of traffic flow in the phase space firstly, and the correlative information in the traffic flow is extracted richly, on the basis of it, a predicted equation for the reconstructed information is established by using chaotic theory, and for the purpose of obtaining the optimal predicted results, recognition and optimization to the model parameters are done by using genetic algorithm. Practical prediction research of urban traffic flow shows that this model has famous predicted precision, and it can provide exact reference for urban traffic programming and control.

在快速变化面前

现实世界的一切都在不断变化，而许多变化又具有“快速、跳跃、复杂”的显著特点。对许多公司和企业来讲，或许它们还不知道如何应对这些“变化”，更不懂在快速变化的环境中如何对策、如何生存、如何发展。

A Molecular Thermodynamic Model for Interfacial Tension in Surfactant-Oil-Water System

An interfacial equation of state based on perturbation theory for surfactant-oil-water system has been developed. By combining the interfacial equation of state with Boudh-Hir and Mansoori's model, a molecular ther-modynamic model has been proposed. The interfacial tension of surfactant-oil-water systems can be calculated from the surface tensions of pure oil and water by this model. The interfacial tension data for sodium dodecyl sulphate-heptane-water system, polyoxyethylene n-octylphenol-heptane-water system and hexadecyl trimethyl ammonium bromide-heptane-water system have been correlated. By using the adjustable parameters obtained, the interfacial tensions of these systems at other temperatures have been predicted. Both the correlated and the predicted values are satisfactory.

Anti-control and Generalized Synchronization of Chaos for a Kind of n-Dimensional Linear Differential System

This paper introduces the finding of some chaotic attractors in a kind of n-dimensional autonomous hybrid system, which is realized via applying some discontinuous state feedback to a kind of n linear differential system. And a constructive theorem is proposed for generalized synchronization related to the above chaotic hybrid systems. Examples are presented for illustrating the methods.

Control of Spiral Waves and Spatiotemporal Chaos by Exciting Travel Wave Trains

Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.

Controlling Chaotic Behavior in a Bose-Einstein Condensate with Linear Feedback

The spatial structure of a Bose-Einstein condensate （BEC） loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.

Application of chaotic theory to parameter estimation

High precision parameter estimation is very important for control system design and compensation. This paper utilizes the properties of chaotic system for parameter estimation. Theoretical analysis and experimental results indicated that this method has extremely high sensitivity and resolving power. The most important contribution of this paper is apart from the traditional engineering viewpoint and actualizing parameter estimation just based on unstable chaotic systems.

Dynamic Equations and Nonlinear Dynamics of Cascade Two-Photon Laser

We derive equations and study nonlinear dynamics of cascade two-photon laser, in which the electromagnetic field in the cavity is driven by coherently prepared three-level atoms and classical field injected into the cavity. The, dynamic equations of such a system are derived by using the technique of quantum Laugevin opera.tots, and then arre studied numerically under different driving＂ conditions, The results show that trader certain conditions the cascade twophoton laser can generate chaotic, period doubling, periodic populations, atomic coherences, and injected classical field, stable and bistable states. Chaos can be inhibited by atomic In ,addition, no chaos occurs in optical bista.bility.

Nonlinear model predictive control based on hyper chaotic diagonal recurrent neural network

Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was proposed for modeling and predicting the behavior of the under-controller nonlinear system in a moving forward window.In order to improve the convergence of the parameters of the HCDRNN to improve system’s modeling,the extent of chaos is adjusted using a logistic map in the hidden layer.A novel NMPC based on the HCDRNN array(HCDRNN-NMPC)was proposed that the control signal with the help of an improved gradient descent method was obtained.The controller was used to control a continuous stirred tank reactor(CSTR)with hard-nonlinearities and input constraints,in the presence of uncertainties including external disturbance.The results of the simulations show the superior performance of the proposed method in trajectory tracking and disturbance rejection.Parameter convergence and neglectable prediction error of the neural network(NN),guaranteed stability and high tracking performance are the most significant advantages of the proposed scheme.

Pattern formation in mutation of “Game of Life”

This paper presents pattern formation in generalized cellular automata (GCA) by varying parameters of classic “game of life”. Different dynamic behaviors are classified. The influence of remembrance of dynamic behavior of GCA is also studied. Experiments show the emergence of the self-organizing patterns that is analogous with life forms at the edge of chaos, which consist of certain nontrivial structure and go through periods of growth, maturity and death. We describe these experiments and discuss their potential as alternative way for creating artificial life and generative art, and as a new method for pattern genesis.

Prediction method for risks of coal and gas outbursts based on spatial chaos theory using gas desorption index of drill cuttings

Based on the evolution of geological dynamics and spatial chaos theory, we proposed the advanced prediction an advanced prediction method of a gas desorption index of drill cuttings to predict coal and gas outbursts. We investigated and verified the prediction method by a spatial series data of a gas desorption index of drill cuttings obtained from the 113112 coal roadway at the Shitai Mine. Our experimental results show that the spatial distribution of the gas desorption index of drill cuttings has some chaotic charac- teristics, which implies that the risk of coal and gas outbursts can be predicted by spatial chaos theory. We also found that a proper amount of sample data needs to be chosen in order to ensure the accuracy and practical maneuverability of prediction. The relative prediction error is small when the prediction pace is chosen carefully. In our experiments, it turned out that the optimum number of sample points is 80 and the optimum prediction pace 30. The corresponding advanced prediction pace basically meets the requirements of engineering applications.

Multi-goal Control of Chaotic Connected Complex Networks

Beam transport network(BTN)with small world(SW)(so-called BTN-SW)and Lorenz chaotic connectednetwork with scale-free(SF)are taken as two typical examples,we proposed a global linear coupling and combined withlocal error feedback methods in sub-networks to realize multi-goal control method of halo and chaos in two networksabove.The simulation results show that the methods above is effective for any chaotic connected networks and has apotential of applications in based-halo-chaos secure communication.

Partition airflow varying features of chaos-theory-based coalmine ventilation system and related safety forecasting and forewarning system

To realize real-time monitoring and short-term forecasting and forewarning of coalmine ventilation systems(CVS), in this paper, we first established a joint surface and underground CVS safety management system consisting of main ventilation fan, safety-partition linked passageways, and air-required locations. We then applied chaos theory to identify the air quantity and gas concentration of underground partition boundaries, and adopted a fixed data quantity, multi-step progressive, weighted first-order local-domain method to setup a chaos prediction model and a CVS safety forecasting and forewarning system formed by the normal change level, orange forewarning level, and red alarm level. We next conduct the on-field application of the system in a coalmine in Jining, Shandong, China. The results showed that (1) in the statistical scale of 5 min, the changes in both air quantity and gas concentration along CVS partition airflow boundaries were characteristic of chaos and could be used for short-term chaos prediction, and the latter was more chaotic than the former;(2) the setup chaos prediction model had a higher prediction precision and the established safety prediction system could not only predict the variation in CVS stability but also reflect the rationality of underground mining intensity. Thus, this CVS safety forecasting and forewarning system is of better application value.

New Predictor-Corrector Methods Based on Exponential Time Differencing forSystems of Nonlinear Differential Equations

We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.

Chaos Analysis of Discharge Current Based on Tracking Test of Phenolic Resin

In tracking test, discharge is a complicated process and comparative tracking index (CTI) has wide varia-tion. To evaluate tracking resistance, the chaos analysis of discharge current is presented based on the tracking test of phenolic resin in accordance with IEC60112. According to the characteristics of statistical self-similarity and complexity of discharge current, the largest Lyapunov exponent is calculated, and the 2-dimensional attractor of discharge current is reconstructed. Moreover, the attractors of discharge current and recurrence plots of different discharge states are reconstructed. The results indicate that the chaos attractors have different characteristics in evo-lutionary tracks, the topological structure and grain direction of recurrence plots show significant differences. The chaos attractor can describe the tracking process, the recurrence plot can identify the tracking state clearly, while its arithmetic is simple.

Stability of GOY Model Under Modulation of Periodic External Force

There is a phase transition between quasi-periodic state and intermittent chaos in GOY model with a critical value δ0. When we add a modulated periodic externa/force to the system, the phase transition can also be found with a critical value δe. Due to coupling between the force and the intrinsic fluctuation of the velocity on shells in GOY model, the stability of the system has been changed, which results in the variation of the critical value. For proper intensity and period of the force, δe is unequal to δ0. The critical value is a nonlinear function of amplitude of the force, and the fluctuation of the velocity can resonate with the external force for certain period Te.

Comparison of Perturbation Theory and Mean Spherical Approximation Based on Molecular Simulation Data

A comprehensive study on various internal energies for the dipolar hard sphere fluids, including Stockmayer fluids, the mixtures of Lennard-Jones and Stockmayer and Stockmayer fluids and the electrolyte solutions is reported based on the perturbation theory and mean spherical approximation. Compared with the results of molecular simulations, it is shown that the perturbation theory is better than the mean spherical approximation.