Improved PSO algorithm based on chaos theory and its application to design flood hydrograph

The deficiencies of basic particle swarm optimization （bPSO） are its ubiquitous prematurity and its inability to seek the global optimal solution when optimizing complex high-dimensional functions. To overcome such deficiencies, the chaos-PSO （COSPSO） algorithm was established by introducing the chaos optimization mechanism and a global particle stagnation-disturbance strategy into bPSO. In the improved algorithm, chaotic movement was adopted for the particles＇ initial movement trajectories to replace the former stochastic movement, and the chaos factor was used to guide the particles＇ path. When the global particles were stagnant, the disturbance strategy was used to keep the particles in motion. Five benchmark optimizations were introduced to test COSPSO, and they proved that COSPSO can remarkably improve efficiency in optimizing complex functions. Finally, a case study of COSPSO in calculating design flood hydrographs demonstrated the applicability of the improved algorithm.

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlin- ear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester （MOA） is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifur- cations such as period doubling bifurcation （PDB）, saddle node bifurcation （SNB）, Hopf bifurcation （HB）, and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are il- lustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.

Arrhythmia Detection by Using Chaos Theory with Machine Learning Algorithms

Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-series data.The second method classifies the ECG by patient experience.The third technique translates ECG impulses into Q waves,R waves and S waves(QRS)features using richer information.Because ECG signals vary naturally between humans and activities,we will combine the three feature selection methods to improve classification accuracy and diagnosis.Classifications using all three approaches have not been examined till now.Several researchers found that Machine Learning(ML)techniques can improve ECG classification.This study will compare popular machine learning techniques to evaluate ECG features.Four algorithms—Support Vector Machine(SVM),Decision Tree,Naive Bayes,and Neural Network—compare categorization results.SVM plus prior knowledge has the highest accuracy(99%)of the four ML methods.QRS characteristics failed to identify signals without chaos theory.With 99.8%classification accuracy,the Decision Tree technique outperformed all previous experiments.

A Color Image Encryption Scheme Based on Singular Values and Chaos

The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication medium where it could be intercepted by unauthorized entities.This study provides an approach to color image encryption that could find practical use in various contexts.The proposed method,which combines four chaotic systems,employs singular value decomposition and a chaotic sequence,making it both secure and compression-friendly.The unified average change intensity,the number of pixels’change rate,information entropy analysis,correlation coefficient analysis,compression friendliness,and security against brute force,statistical analysis and differential attacks are all used to evaluate the algorithm’s performance.Following a thorough investigation of the experimental data,it is concluded that the proposed image encryption approach is secure against a wide range of attacks and provides superior compression friendliness when compared to chaos-based alternatives.

Hybrid optimization algorithm based on chaos,cloud and particle swarm optimization algorithm

As for the drop of particle diversity and the slow convergent speed of particle in the late evolution period when particle swarm optimization（PSO） is applied to solve high-dimensional multi-modal functions,a hybrid optimization algorithm based on the cat mapping,the cloud model and PSO is proposed.While the PSO algorithm evolves a certain of generations,this algorithm applies the cat mapping to implement global disturbance of the poorer individuals,and employs the cloud model to execute local search of the better individuals;accordingly,the obtained best individuals form a new swarm.For this new swarm,the evolution operation is maintained with the PSO algorithm,using the parameter of pop distr to balance the global and local search capacity of the algorithm,as well as,adopting the parameter of mix gen to control mixing times of the algorithm.The comparative analysis is carried out on the basis of 4 functions and other algorithms.It indicates that this algorithm shows faster convergent speed and better solving precision for solving functions particularly those high-dimensional multi-modal functions.Finally,the suggested values are proposed for parameters pop distr and mix gen applied to different dimension functions via the comparative analysis of parameters.

Optimization of HMM Parameters Based on Chaos and Genetic Algorithm for Hand Gesture Recognition

In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA, thus forming chaotic anneal genetic algorithm (CAGA). Chaos ergodicity is used to initialize the population, and chaotic anneal mutation operator is used as the substitute for the mutation operator in SGA. CAGA is a unified framework of the existing chaotic mutation methods. To validate the proposed algorithm, three algorithms, i. e. Baum-Welch, SGA and CAGA, are compared on training hidden Markov model (HMM) to recognize the hand gestures. Experiments on twenty-six alphabetical gestures show the CAGA validity.

Chaos-Based Multipurpose Image Watermarking Algorithm

To achieve the goal of image content authentication and copyright protection simultaneously, this paper presents a novel image dual watermarking method based on chaotic map. Firstly, the host image was split into many nonoverlapping small blocks, and the block-wise discrete cosine transform （DCT） is computed. Secondly, the robust watermarks, shuffled by the chaotic sequences, are embedded in the DC coefficients of blocks to achieve the goal of copyright protection. The semi-fragile watermarks, generated by chaotic map, are embedded in the AC coefficients of blocks to obtain the aim of image authentication. Both of them can be extracted without the original image. Simulation results demonstrate the effectiveness of our algorithm in terms of robustness and fragility.

Feedback Control of Chaos in Delay Maps

In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The control is achieved by using small, bounded perturbations. Some numerical simulations are given to demonstrate the effectiveness of the proposed control method.

NON-INTEGRABILITY AND CHAOS OF A CONSERVATIVE COMPOUND PENDULUM

By using a series of canonical transformations (Birkhoff's series), an approximate integral of a conservative compound pendulum is evaluated. Level lines of this approximate integral are compared with the numerical simulation results. It is seen clearly that with a raised energy level, the nearly integrable system becomes non-integrable, i.e. the regular motion pattern changes to the chaotic one. Experiments with such a pendulum device display the behavior mentioned above.

PANSYSTEMS LOGIC CONSERVATION OF BIFURCATION,CATASTROPHE,CHAOS AND STABILITY

It was shown in Wu's works that the combination of the relative researches of pansystems methodology and the researches on bifurcation, catastrophe, chaos and stability in nonlinear mechanics was put forward and the concepts were redefined from the point of view of pansystems methodology. In this paper, the logic conservation law of these nonlinear mechanics phenomena was studied under the framework of pansystems methodology.

COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS

This paper discusses the dynamic behavior of the Kelvin-Stuart cat's eye flow under periodic perturbations. By means of the Melnikov method the conditions to have bifurcations to subharmonics of even order for the oscillating orbits and to have bifurcations to subharmonics of any order for the rotating orbits are given, and further, the coexistence phenomena of the chaotic motions and periodic solutions are presented.

Chaos in Time Series of Sakarya River Daily Flow Rate

In this study, possible low dimensional chaotic behavior of Sakarya river flow rates is investigated via nonlinear time series techniques. To reveal the chaotic dynamics, the maximal positive Lyapunov exponent is calculated from the reconstructed phase space, which is obtained using the phase space reconstruction method. The method reconstructs a phase space from the scalar time series, which depicts the real system’s invariants Positive values, because the Lyapunov exponent values calculated using the appropriate software program indicate possibility of chaotic behavior. Analyzed data involve the monthly average flow rates of eleven main branches of Sakarya River through the years 1960-2000.

Freud’s Theory and the Group Mind Theory:Formulations

This study aimed to reconsider some concepts of the psychoanalytic theory on group mind. Group psychology is concerned with the individual man as a member of a race, nation, caste, profession, or an institution, or as a component of a crowd of people that has been organized into a group at some particular time, for some specific purpose. Group psychology embraces an immense number of separate issues and offers investigators with countless problems, which have hitherto not even been properly distinguished from one another. Reflections presented in this paper were particularly inspired by Freud’s work on Group psychology and analysis of the ego and approaches to the chaos theory, especially, the fact that groups emerge as systems that exhibit unstable, aperiodic and highly complex behavior, with a tendency to self-organization.

A Novel 2D Hyperchaotic with a Complex Dynamic Behavior for Color Image Encryption

The generation method of the key stream and the structure of the algorithm determine the security of the cryptosystem.The classical chaotic map has simple dynamic behavior and few control parameters,so it is not suitable for modern cryptography.In this paper,we design a new 2D hyperchaotic system called 2D simple structure and complex dynamic behavior map(2D-SSCDB).The 2D-SSCDB has a simple structure but has complex dynamic behavior.The Lyapunov exponent verifies that the 2D-SSCDB has hyperchaotic behavior,and the parameter space in the hyperchaotic state is extensive and continuous.Trajectory analysis and some randomness tests verify that the 2D-SSCDB can generate random sequences with good performance.Next,to verify the excellent performance of the 2D-SSCDB,we use the 2D-SSCDB to generate a keystream for color image encryption.In the encryption algorithm,the encryption algorithm scrambles and diffuses simultaneously,increasing the cryptographic system’s security.The horizontal correlation,vertical correlation,and diagonal correlation of ciphertext are−0.0004,−0.0004 and 0.0007,respectively.The average information entropy of the ciphertext is 7.9993.In addition,the designed encryption algorithm reduces the correlation between the three channels of the color image.Security analysis shows that the color image encryption algorithm designed using 2DSSCDB has good security,can resist standard attack methods,and has high efficiency.

A Cross-Plane Color Image Encryption Algorithm Based on 1D-SLM

With the rapid development of 5G technology,it has become fast and easy for people to transmit information on the Internet.Digital images can express information more intuitively,so transmitting information through images has excellent applications.This paper uses a new chaotic system called 1D-Sin-Logistic-Map(1D-SLM).1D-SLM has two control parameters,which can provide larger parameter space,and the parameter space in the chaotic state is continuous.Through Lyapunov exponent analysis(LE),bifurcation diagrams analysis,spectral entropy analysis(SE),and 0-1 test,it is verified that 1D-SLM has complex dynamic behavior and is very suitable for cryptography.Compared with other 1D chaotic systems,the 1D-SLM has a larger Lyapunov exponent(LE)and spectral entropy(SE).For color image encryption algorithms,only relying on chaotic mapping is not enough to ensure security.So combined with 1D-SLM,we design a color image encryption algorithm,which is implemented by plane expansion,which reduces the correlation between the three channels of color images.The experimental results show that the proposed cross-plane color image encryption algorithm is safe and resistant to common attack methods.

3D Model Encryption Algorithm by Parallel Bidirectional Diffusion and 1D Map with Sin and Logistic Coupling

3D models are essential in virtual reality,game development,architecture design,engineering drawing,medicine,and more.Compared to digital images,3D models can provide more realistic visual effects.In recent years,significant progress has been made in the field of digital image encryption,and researchers have developed new algorithms that are more secure and efficient.However,there needs to be more research on 3D model encryption.This paper proposes a new 3D model encryption algorithm,called the 1D map with sin and logistic coupling(1D-MWSLC),because existing digital image encryption algorithms cannot be directly applied to 3D models.Firstly,this paper introduce 1D-MWSLC,which has a wider range of parameters compared to traditional 1D chaotic systems.When the parameter exceeds a specific range,the chaotic phenomenon does not weaken.Additionally,1D-MWSLC has two control parameters,which increases the cryptosystem’s parameter space.Next,1D-MWSLC generates keystreams for confusion and diffusion.In the confusion stage,this paper use random confusion,and the keystream generates an index matrix that confuses the integer and decimal parts of the 3D model simultaneously.In the diffusion stage,this paper use parallel bidirectional diffusion to simultaneously diffuse the integer parts of the three coordinates of the 3D model.Finally,this paper verify the proposed algorithm through statistical analysis,and experimental results demonstrate that the proposed 3D model encryption algorithm has robust security.

Prediction Model of Weekly Retail Price for Eggs Based on Chaotic Neural Network

This paper establishes a short-term prediction model of weekly retail prices for eggs based on chaotic neural network with the weekly retail prices of eggs from January 2008 to December 2012 in China.In the process of determining the structure of the chaotic neural network,the number of input layer nodes of the network is calculated by reconstructing phase space and computing its saturated embedding dimension,and then the number of hidden layer nodes is estimated by trial and error.Finally,this model is applied to predict the retail prices of eggs and compared with ARIMA.The result shows that the chaotic neural network has better nonlinear fitting ability and higher precision in the prediction of weekly retail price of eggs.The empirical result also shows that the chaotic neural network can be widely used in the field of short-term prediction of agricultural prices.

CHAOTIC BEHAVIOR OF A NONLINEAR OSCILLATOR

The behavior of bifurcation and chaos in a forced oscillator containing a square nonlinear term was investigated by using Mel'nikov method and digital computer simulations. It was show that the system blows up for low damping before the motion develops into chaotic one when frequency is locked. The routes which lead to chaos are different for different frequency. After the parameters cross chaotic zone, the response of the system are also different. The three cases all depend on the values of dumping and frequency.

Kinematic Analysis of the Neck and Upper Extremities During Walking in Healthy Young Adults

The objective of this paper is to quantify the local stabilities of the neck and upper extremities （right/left shoulders and right/left elbows）, and investigate differences between linear and nonlinear measurements of the associated joint motions and differences in the local stability between the upper and lower extremities. This attempt involves the calculation of a nonlinear parameter, Lyapunov Exponent （LE）, and a linear parameter, Range of Motion （ROM）, during treadmill walking in conj unction with a large population of healthy subjects. Joint motions of subjects were captured using a three-dimensional motion-capture system. Then mathematical chaos theory and the Rosenstein algorithm were employed to calculate LE of joints as the extent of logarithmic divergence between the neighboring state-space trajectories of flexion-extension angles. LEs computed over twenty males and twenty females were 0.037~0.023 for the neck, 0.043＋0.021 for the right shoulder, 0.045i0.030 for the left shoulder, 0.032i0.021 for the right elbow, and 0.034~0.026 for the left elbow. Although statistically significant difference in the ROM was observed between all pairs of the neck and upper extremity joints, differences in the LE between all pairs of the joints as well as between males and females were not statistically significant. Between the upper and lower extremities, LEs of the neck, shoulder, and elbow were significantly smaller than those of the hip （-0.064） and the knee （-0,062）. These results indicate that a statistical difference in the local stability between the upper extremity joints is not significant. However, the different result between the ROM and LE gives a strong rationale for applying both linear and nonlinear tools together to the evaluation of joint movement. The LEs of the joints calculated from a large population of healthy subjects could provide normative values for the associated joints and can be used to evaluate the recovery progress of patients with joint related diseases.

High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and irregularities.The change tendency may be related to the occurrence of earthquake disasters.Forecasting of the underlying intensity trend plays an important role in the analysis of data and disaster monitoring.Combining chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field signal.The main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field data.In verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data respectively.According to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function model.Hence,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.