含有混沌量的IS-LM模型及其均衡性质研究

利用结构乘数的概念及其表达式,得到含有逻辑斯蒂映射的动态边际消费倾向方程,再通过将IS-LM模型动态化的方法推导出含有混沌量的IS-LM模型。研究结果表明:两个市场同时均衡的一般均衡点并不是唯一的。当参数处在一定范围时,会有多个一般均衡点;均衡点还可以处在混沌区内,此时均衡点可以有无穷多个。

APPLICATION OF CHAOS IN MEASUREMENT

Using the high sensitivity to initial values of chaotic systems, this paper describes an application of chaos in the field of measurement. A general method for signal coding based on symbolic sequences and the relationship between the variable (to be measured) and its symbolic sequence are presented. Some performances of the chaos based measurement system are also discussed. Theoretical analysis and experimental results show that chaotic systems are potentially attractive in the field of measurement.

基于杂草算法的配电网光伏电源优化研究

本文针对配电网光伏电源渗透率低和损耗高的问题,在以配电网光伏电源配置多目标模型为基础上引进了改进杂草算法的目标函数求解方法。其中,在标准的杂草算法的基础上,利用分散播种和添加混沌扰动量对其进行改进,然后以IEEE33节点系统为例,用改进后的杂草算法对配电网光伏电源的配置进行优化。仿真实验表明,改进后的杂草算法对光伏电源配置的多目标化模型求解,可以有效的提高光伏电源渗透率,和降低配电网工作中的损耗,可以更好的改善配电网的电压质量。通过以上优化,证明杂草算法可求解得到光伏电源配置的最优解,提高光伏电源渗透率低,降低损耗,具有一定的可行性。

A new optimization algorithm based on chaos

In this article, some methods are proposed for enhancing the converging velocity of the COA (chaos optimization algorithm) based on using carrier wave two times, which can greatly increase the speed and efficiency of the first carrier wave’s search for the optimal point in implementing the sophisticated searching during the second carrier wave is faster and more accurate. In addition, the concept of using the carrier wave three times is proposed and put into practice to tackle the multi-variables opti- mization problems, where the searching for the optimal point of the last several variables is frequently worse than the first several ones.

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.

Application of Extended Kalman Filter to the Modeling of Electric Arc Furnace for Power Quality Issues

Electric arc furnaces(EAFs)represent one of the most disturbing loads in the subtransmission or transmission electric power systems.Therefore,it is necessary to build a practical model to descript the behavior of EAF in the simulation of power system for power quality issues.This paper deals with the modeling of EAF based on the combination of extended Kalman filter to identify the parameter of arc current and the power balance equation to obtain the dynamic,multi-valued u-i characteristics of EAF load.The whole EAF systems are simulated by means of power system blockset in Matlab to validate the proposed EAF model.This model can also be used to assess the impact of the new plant or highly varying nonlinear loads that exhibit chaos in power systems.

Generalized Synchronization Between Different Fractional-Order Chaotic Systems

In this paper,using scalar feedback controller and stability theory of fractional-order systems,a gener-alized synchronization method for different fractional-order chaotic systems is established.Simulation results show theeffectiveness of the theoretical results.

Chaotic phenomenon and the maximum predictable time scale of observation series of urban hourly water consumption

The chaotic characteristics and maximum predictable time scale of the observation series of hourly water consumption in Hangzhou were investigated using the advanced algorithm presented here is based on the conventional Wolf's algorithm for the largest Lyapunov exponent. For comparison, the largest Lyapunov exponents of water consumption series with one-hour and 24-hour intervals were calculated respectively. The results indicated that chaotic characteristics obviously exist in the hourly water consumption system; and that observation series with 24-hour interval have longer maximum predictable scale than hourly series. These findings could have significant practical application for better prediction of urban hourly water consumption.

Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.

Construction and Verification of a Simple Smooth Chaotic System

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equilibrium points respectively. Dynamical properties of this system are then studied. Furthermore, by applying the undetermined coefficient method, heteroclinic orbit of Shil＇nikov＇s type in this system is found and the convergence of the series expansions of this heteroclinic orbit are proved in this article. The Shil＇nikov＇s theorem guarantees that this system has Smale horseshoes and the horseshoe chaos.

Deformation prediction of tunnel surrounding rock mass using CPSO-SVM model

A new method integrating support vector machine (SVM),particle swarm optimization (PSO) and chaotic mapping (CPSO-SVM) was proposed to predict the deformation of tunnel surrounding rock mass.Since chaotic mapping was featured by certainty,ergodicity and stochastic property,it was employed to improve the convergence rate and resulting precision of PSO.The chaotic PSO was adopted in the optimization of the appropriate SVM parameters,such as kernel function and training parameters,improving substantially the generalization ability of SVM.And finally,the integrating method was applied to predict the convergence deformation of the Xiakeng tunnel in China.The results indicate that the proposed method can describe the relationship of deformation time series well and is proved to be more efficient.

Control of a Unified Chaotic System via Single Variable Feedback

Based on the LaSalle invariance principle, we propose a simple adaptive-feedback for controlling the unified chaotic system. We show explicitly with numerical proofs that our method can easily achieve the control of chaos in the unified chaotic system using only a single variable feedback. The present controller, to our knowledge, is the simplest control scheme for controlling a unified chaotic system.

Human action recognition based on chaotic invariants

A new human action recognition approach was presented based on chaotic invariants and relevance vector machines(RVM).The trajectories of reference joints estimated by skeleton graph matching were adopted for representing the nonlinear dynamical system of human action.The C-C method was used for estimating delay time and embedding dimension of a phase space which was reconstructed by each trajectory.Then,some chaotic invariants representing action can be captured in the reconstructed phase space.Finally,RVM was used to recognize action.Experiments were performed on the KTH,Weizmann and Ballet human action datasets to test and evaluate the proposed method.The experiment results show that the average recognition accuracy is over91.2%,which validates its effectiveness.

Intelligent prediction on air intake flow of spark ignition engine by a chaos radial basis function neural network

To ensure the control of the precision of air-fuel ratio(AFR)of port fuel injection(PFI)spark ignition(SI)engines,a chaos radial basis function(RBF)neural network is used to predict the air intake flow of the engine.The data of air intake flow is proved to be multidimensionally nonlinear and chaotic.The RBF neural network is used to train the reconstructed phase space of the data.The chaos algorithm is employed to optimize the weights of output layer connection and the radial basis center of Gaussian function in hidden layer.The simulation results obtained from Matlab/Simulink illustrate that the model has higher accuracy compared to the conventional RBF model.The mean absolute error and the mean relative error of the chaos RBF model can reach 0.0017 and 0.48,respectively.

Fuzzy least squares support vector machine soft measurement model based on adaptive mutative scale chaos immune algorithm

In order to enhance measuring precision of the real complex electromechanical system,complex industrial system and complex ecological & management system with characteristics of multi-variable,non-liner,strong coupling and large time-delay,in terms of the fuzzy character of this real complex system,a fuzzy least squares support vector machine(FLS-SVM) soft measurement model was established and its parameters were optimized by using adaptive mutative scale chaos immune algorithm.The simulation results reveal that fuzzy least squares support vector machines soft measurement model is of better approximation accuracy and robustness.And application results show that the relative errors of the soft measurement model are less than 3.34%.

Using chaos to improve measurement precision

If the measuring signals were input to the chaotic dynamic system as initial parameters, the system outputs might be in steady state, periodic state or chaos state. If the chaotic dynamic system outputs controlled in the periodic states, the periodic numbers would be changed most with the signals. Our novel method is to add chaotic dynamic vibration to the measurement or sensor system.The sensor sensitivity and precision of a measurement system would be improved with this method. Chaotic dynamics measurement algorithms are given and their sensitivity to parameters are analyzed in this paper. The effects of noises on the system are discussed.

Structure of Hamiltonian Matrix and the Shape of Eigenfunctions：Nuclear Octupole Deformation Model

The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.

Short-Term Forecasting of Urban Water Consumption Based on the Largest Lyapunov Exponent

An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were examined by means of the largest Lyapunov exponent and correlation dimension. By using the largest Lyapunov exponent a short-term forecasting model for urban water consumption was developed, which was compared with the artificial neural network (ANN) approach in a case study. The result indicates that the model based on the largest Lyapunov exponent has higher prediction precision and forecasting stability than the ANN method, and its forecasting mean relative error is 9.6% within its maximum predictable time scale while it is 60.6% beyond the scale.

Energy Level Statistics in Particle—Rotor Model

Energy level statistics of a system consisting of six particles interacting by delta force in a two- model coupled with a deformed core is studied in particle-rotor model. For single- shell and two- shell the exact energies for our statistical analysis are obtained from a full diagonalization of the Hamiltonian, while in two- case the configuration truncation is used. The nearest-neighbor distribution of energy levels and spectral rigidity are studied as the function of spin. The results of single- shell are compared with those in two- case. It is showed that the system becomes more regular when single- space is replaced by two- shell although the basis size of the configuration space is unchanged. The degree of chaoticity of the system, however, changes slightly when configuration space is enlarged by extending single- shell to two- shell .

Chaotic Control of Network Traffic

This paper presents a chaotic control method on network traffic. By this method, the chaotic network traffic can be controlled to pre-assigned equifibrium point according to chaotic prediction and the Largest Lyapunov Exponent （LLE） of the traffic on congested link is reduced, thereby the probability of traffic burst and network congestion can be reduced. Numerical examples show that this method is effective.