Application Of Chaos Theory Research Articles

The theory of dynamic chaos in the socio-philosophical and social studies

The article discusses the application of the theory of dynamic chaos to the study of social phenomena. Appeal to the origins of the creation of the theory of dynamic chaos in natural science (A. Poincaré, I. Prigogine, E. Lorenz, and others) revealed nonlinear dynamic systems in the natural environment (turbulent flows, atmosphere, biological populations, etc.). The category of “chaos” is now firmly established in the arsenal of the social sciences and humanities, although only recently it referred exclusively to natural science knowledge (the theory of chaos in mathematics, physics, biology, etc.). In synergetics, for the first time, the description of self-organization processes as a mutual transition of order and chaos was proposed by I.R. Prigogine.But in the social sciences such systems are society, its economic, political and other spheres, which have the properties of non-closure, instability and non-linear development. In Ukrainian philosophical thought, one of the first works in which the problem of the development of nonlinear self-developing systems was highlighted was the work of I.S. Dobronravova (1991). Scientific monograph I.V. Yershova-Babenko (1992) also had a significant impact on the development of studies of complex non-linear systems, since for the first time the system of the human psyche was considered as a non-linear self-organized system. The psycho-synergetic model of social reality is based on the fact that social reality is a psychomeric environment, i.e. a complex nonlinear system consisting of other complex nonlinear integrity, which are determined by phase transitions between different states of chaos and order. The application of chaos theory is also possible at the micro and macro levels of social research, which is presented by Ukrainian researchers in synergetics (I. S. Dobronravova, L. Finkel) and in psychosynergetics (I.V. Yershova-Babenko), L. Bevzenko and others.

Application of Chaos Theory in Incomplete Randomized Financial Analysis

In the new economy, some tech companies have rapidly built market power and modernization led to the unpredictable bank-to-client relationship. Moreover, financial markets are confronted with big data and as a result, digitization and further introduction of mathematical techniques and new models were brought into the financial industry. Uncertainty has increased markedly in the macroeconomic risk, payment systems, capital accumulation and investment. But so far, timid attempts are made to elucidate the possibilities of the chaos theory application in finance. To verify a theoretical model whether or not is an accurate representation of an empirically observed phenomenon is one of the most challenging investigations in the scientific field. The following study explores the problem related to incomplete randomized financial analysis. The behavior of financial market relates to the circumstances that are both internal and external. Chaos mathematics is an acute methodology to be applied in the analysis of the randomness in financial markets instead of completely randomized design. The completely randomized design places the emphasis on which the factor effects are constant and assumes the observation from experiments to be statistically independent. However, this hypothesis is often not realistic and practical. The correlated impact should not be ignored. This article attempts to clarify some points related to the possibility of using chaos theory in finance.

Application of chaos theory to optimize the running-in parameters by using a running-in attractor

The running-in quality and efficiency could be improved by optimizing load, velocity and initial surface roughness of contact surfaces. The relationship between characteristic parameters of running-in attractor and running-in quality was studied. Theoretical analysis and experimental results show that the greater the correlation dimension, the less the enclosing radius, the better the running-in quality. Taking correlation dimension, enclosing radius and running-in time as three objectives, the multi-objective optimization was carried out by using the elitist non-dominated sorting genetic algorithm. The optimal running-in parameter set for AISI 52100-AISI 1045 system were obtained. According to the computed results, the harder surface should be machined to a less roughness, while the roughness of softer surface could be selected in a relatively wider range. For softer surface, a combination of great roughness and great load or velocity should be avoided in order to ensure running-in quality, and a combination of small roughness and small load or velocity should be avoided in order to ensure running-in efficiency. The proposed method provides reference for optimizing running-in parameters of other friction systems.

On the correlation of chaotic signals generated by multimodal skew tent map

In recent years, a great deal of attention has been devoted to the application of chaos theory in signal processing and communications. Despite the importance of spectral analysis in these domains, there are few works that take an interest in spectral properties of chaotic signals. In this work, we derive analytic expressions for the autocorrelation function and the auto-spectral density function of chaotic signals generated by a multimodal skew tent map. Our results reveal that chaotic signals generated from a multimodal skew tent map have similar spectral properties to those generated from a unimodal skew tent map.

Application of chaos theory to the particle dynamics of asymmetry-induced transport

The techniques of chaos theory are employed in an effort to better understand the complex single-particle dynamics of asymmetry-induced transport in non-neutral plasmas. The dynamical equations are re-conceptualized as describing time-independent trajectories in a four-dimensional space consisting of the radius r, rotating frame angle ψ, axial position z, and axial velocity v. Results include the identification of an integral of the motion, fixed-point analysis of the dynamical equations, the construction and interpretation of Poincaré sections to visualize the dynamics, and, for the case of chaotic motion, numerical calculation of the largest Lyapunov exponent. Chaotic cases are shown to be associated with the overlap of resonance islands formed by the applied asymmetry.

An examination of initiation rituals in a UK sporting institution and the impact on group development

ABSTRACTResearch question: This study investigates the impact of initiation rituals on group development. Through the application of chaos theory, we examine how the trajectory of team development is inherently unpredictable due to the complex nature and uncertainty of initiation rituals.Research methods: The paper draws upon 42 interviews with student athletes from a UK university. The UK context provides a new perspective on initiation activities that are currently dominated by studies in a US setting.Results and findings: From our coding of interview data four themes emerge: Forced assimilation, Dejection, Commitment, and Performance. The results find initiation rituals force sport teams into a period of chaos where outcomes can vary from improved performance to dejection. Thus, sports teams can experience any, or all of the themes present in our findings, and previous group cohesion is an unreliable predictor for successful group development post-initiation.Implications: Theoretically, we further understanding of group development as an unpredictable system due to the nuances and complexities associated with initiations that stimulate periods of chaos. Practically we find administration of bureaucratic control is an ineffective mechanism for constraining initiation activities, and instead it is team leaders and captains who should guide behaviour towards constructive and enjoyable initiations associated with improved commitment and performance of sporting teams.

Characterization of Chaotic Electro Optic Modulator with the Helpof Lyapunov Exponent and Bifurcation Analysis Technique.

Chaos is a fundamental property that comes out of nonlinearity and a sensitive dependence on initial condition. A nonlinear dynamic system that displays a chaotic steady state behaviour is purely deterministic, but its long-term behaviour cannot be predicted because of the property of sensitivity to initial conditions. One of the most promising applications of chaos theory, which exploits both the deterministic and unpredictable aspects of chaotic behaviour, is chaos-based secure communications. The sensitivity to initial condition is quantified with the help of the entropy named Lyapunov Exponent. Generation of chaos from nonlinear optical devices have been explored from several years. In this paper an EO modulator system of cos2 type of nonlinearity is selected as chaos producing device and characterized with the help of Lyapunov Exponent. The Lyapunov Exponent is computed here to determine the dependence of a chaotic signal on the initial conditions and also on the system parameters. The period doubling behaviour in this Electro optic modulator system have also been studied here. The transition from periodic to chaotic behaviours in this one-dimensional discrete dynamical system have been controlled through variation of a single parameter out of different system parameters. With the help of Lyapunov Exponent and bifurcation analysis technique an estimation of the system parameters has been carried out to predict the nature of the output generated at the terminal of the EO cell.

THE EFFECT OF CHAOS THEORY ON THE PREDICTABILITY OF THE ATMOSPHERE

It is known that atmosphere is a dynamical system that constantly changing and moving. It is a very difficult problem to completely determine and explain the change in the atmosphere. But the mathematical models can help us to understand and explain the dynamical processes in the atmosphere. Examination of the movements of the atmosphere is one of the most exciting applications of chaos theory. The main goals of this presentation will be try to discuss the effect of chaos theory on the predictability of the atmosphere. For this purpose, we focus on one of the most specific examples of atmosphere events, is global climate change.

Diagnosing ASD with fractal analysis

PurposeNeuroscience is providing new tools to potentially improve diagnosis and classification of autism spectrum disorder (ASD) based on biomarkers. The purpose of this paper, is to describe certain applications of fractal analysis, a tool used to measure information complexity observed within electroencephalograph (EEG) signals and neurogenetic code. It is argued here that a better method of diagnosis of ASD may exist based on these new tools.Design/methodology/approachSelective review of literature focused on the diagnosis of ASD and recent technological advances in scientific approaches to diagnosis of ASD. It is argued that higher levels of complex, coherent data are inversely related to pathology; in biological systems, lower complexity EEG during specific tasks may reveal pathology.FindingsClinicians and researchers are exploring new ways to describe mental illness based on biomarkers to improve reliability and validity of diagnostic methods. Specific application of chaos theory in the form of fractal analysis shows promise as one possible method.Originality/valueThis is a conceptual paper addressing the advantages of employing fractal analysis of EEG and genomics for the diagnosis of ASD.

GRAMMATICALIZATION PATHS AND CHAOS: DETERMINISM AND UNPREDICTABILITY OF THE SEMANTIC DEVELOPMENT OF VERBAL CONSTRUCTIONS (PART 3 – CHAOS IN GRAMMATICALIZATION)

This paper demonstrates that by applying Chaos Theory to the modelling of the evolution of verbal forms and verbal systems, it is possible to view classical grammaticalization paths as universal, and align this deterministic assumption with the unpredictability of concrete grammatical developments. The author argues that such an explanation is possible because traditional grammaticalization paths do not represent realistic cases of grammatical evolutions, but rather correspond to abstract and non-realistic deterministic laws which codify the order of the incorporation of new meanings to the semantic potential of a gram. Therefore, from a synchronic perspective, they can be used to represent the semantic potential of a form as a map or a state. In contrast, a realistic development emerges as a trajectory connecting such maps or states. Consequently, the cross-linguistic typological model of realistic evolutionary processes of a certain type corresponds to a state-space – it is a cluster of all possible trajectories the grams of a certain class can travel. This article – the second of series of three papers – will deal with a principled application of Chaos Theory to linguistics and with a new alternative interpretation of paths postulated by Path Theory.

Application of chaos theory in data security-a survey

Application of chaos theory in data security-a survey

Surface investigation by electrochemical methods and application of chaos theory and fractal geometry

The present study has considered the application of the noise analysis and fractal geometry as a promising dynamic method for exploiting the corrosion mechanism of the stainless steel 304 that is immersed in different concentrations of FeCl3. The fractal dimension calculated from the electrochemical noise technique has a good correlation with the surface fractal dimension obtained by electrochemical impedance spectroscopy and scanning electron microscopy results. The complexity of system increases by divergence of Electrochemical Potential noise fractal dimension from 1.5 value and also the roughness of surface increases by an increase in surface fractal dimension. As the concentration of FeCl3 increases (0.001M, 0.01M and 0.1M) the value of Electrochemical Potential noise fractal dimension diverges from 1.5 value (1.57, 1.33 and 1.01 respectively) and the value of surface fractal dimension increases (2.107, 2.425 and 2.756 for impedance results and 2.073, 2.425 and 2.672 for scanning electron microscopy images). These results show that the complexity of system and roughness of the surface increases by an increase in concentration of FeCl3. The present study has shown that chaos and noise analysis are effective methods for the study of the mechanism of the corrosion process.

Do new sources of traffic data make the application of Chaos Theory to traffic management a realistic possibility?

ABSTRACTCurrent signal systems for managing road traffic in many urban areas around the world lack a coordinated approach to detecting the spatial and temporal evolution of congestion across control regions within city networks. This severely inhibits these systems’ ability to detect reliably, on a strategic level, the onset of congestion and implement effective preventative action. As traffic is a time-dependent and non-linear system, Chaos Theory is a prime candidate for application to Urban Traffic Control (UTC) to improve congestion and pollution management. Previous applications have been restricted to relatively uncomplicated motorway and inter-urban networks, arguably where the associated problems of congestion and vehicle emissions are less severe, due to a general unavailability of high-resolution temporal and spatial data that preserve the variability in short-term traffic patterns required for Chaos Theory to work to its full potential. This paper argues that this restriction can now be overcome due to the emergence of new sources of high-resolution data and large data storage capabilities. Consequently, this opens up the real possibility for a new generation of UTC systems that are better able to detect the dynamic states of traffic and therefore more effectively prevent the onset of traffic congestion in urban areas worldwide.

Short-term economic emission power scheduling of hydrothermal systems using improved chaotic hybrid differential evolution

Increasing concerns over atmospheric pollution forces the power-producing utilities to retain their generations within maximum allowable emission levels. Therefore, in present-day power system operations, the minimization of emission pollutants along with the total fuel cost has become an important aspect in short-term generation scheduling of hydrothermal power systems. This paper presents an improved hybrid approach based on the application of chaos theory in a differential evolution (DE) algorithm for the solution of this biobjective constrained optimization problem. In this proposed methodology, self-adjusted parameter setting in DE is obtained by using chaotic sequences. Secondly, a chaotic hybridized local search mechanism is embedded in DE to avoid it from trapping at local optima and to enhance its search space exploring ability. Furthermore, new heuristic strategies are developed to effectively handle the complex hydraulic and thermal constraints. The feasibility and usefulness of the developed approach are demonstrated by its application on a standard hydrothermal test system compromising four multicascaded hydel plants and three thermal plants and the following three case studies are investigated: economic power scheduling, economic emission scheduling, and economic emission power scheduling. The simulation results illustrate the superiority of the proposed approach as compared to other recently established techniques.

The Application of Chaos Theory and Fractal Mathematics to the Study of Cancer Evolution: Placing Metabolism and Immunity Centre Stage

Despite the undoubted triumphs that have occurred in the treatment of some cancers, overall, the outcomes for disseminated disease remain poor. A change in perspective is therefore required to develop more effective treatment strategies. This review provides an overview of the potential contribution of chaos theory and fractal mathematics to the study of cancer evolution. The atavistic model of cancer proposes that cancer represents a reversion to an evolutionarily ancient proliferative phenotype, and suggests that cellular metabolism and the immune system are targets to which cancer may be susceptible. The approaches of chaos theory and fractal mathematics point to the same targets, and the synergy of these two perspectives will be explored. The emerging unifying concept which emerges is that the cellular machinery of the differentiated cell resists entropy in favour of stable structure. Each evolutionary development from multicellular organisms upwards, diverts more energy away from entropy. When malignant transformation occurs, the cell succumbs to the draw of the thermodynamic laws, maximizing fractal entropy, reverting to its ancient proliferative phenotype and moving, in its increased dynamic state, into greater chaos. Changes in the chaotic dynamics of cellular function evolve in parallel with changes in the fractal geometry of cellular structure. If the dynamics of the cancer cell can be worked out mathematically, it may be possible to use these dynamics to plan treatment strategies in the way that chaos theory is currently used to, for example, guide satellites. Although the responses of the tumour to the suggested targets may be weaker, they may also be more sustainable, and produce fewer side effects, than the current modalities and the emerging molecularly targeted therapies.

Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks

In recent times, urban road networks are faced with severe congestion problems as a result of the accelerating demand for mobility. One of the ways to mitigate the congestion problems on urban traffic road network is by predicting the traffic flow pattern. Accurate prediction of the dynamics of a highly complex system such as traffic flow requires a robust methodology. An approach for predicting Motorised Traffic Flow on Urban Road Networks based on Chaos Theory is presented in this paper. Nonlinear time series modeling techniques were used for the analysis of the traffic flow prediction with emphasis on the technique of computation of the Largest Lyapunov Exponent to aid in the prediction of traffic flow. The study concludes that algorithms based on the computation of the Lyapunov time seem promising as regards facilitating the control of congestion because of the technique’s effectiveness in predicting the dynamics of complex systems especially traffic flow.

Application of Chaos Theory for Power Quality Improvement

Application of Chaos Theory for Power Quality Improvement

An overwhelming amount of data: Applying chaos theory to find patterns within big data

This paper introduces basic concepts of chaos theory into the world of big data and real-time big data analysis. It concentrates on demonstrating how chaos theory can be applied to analysing big data, what elements must be present, and what the possible outcomes can be. Although chaos theory contains a few set rules, the paper concentrates on the meaning and importance of the butterfly effect in finding patterns and trends within big data analysis. It should be noted that, although many aspects of the application of chaos theory to big data analytics are largely theoretical or in the infancy of deployment, almost all big data analysing systems active today make use of the essential components contained within chaos theory.

Статистическая и хаотическая оценка параметров кардиоинтервалов в условиях физической нагрузки

Methods of classical statistics and the theory of chaos and self-organization studied the behavior of the vector of the cardiovascular system in groups of students trained and untrained in response to dosed physical stress .It was found that students without physical fitness indicators of cardio area quasi-attractors increased after exercise . The study had shown significant changes in the dynamics of the behavior of the parameters of functional systems of the human body compared to the stochastic approach based on the histogram and Shannon entropy . It is shown the feasibility of application of chaos theory, self-organization in the evaluation of the reaction of the cardiovascular system of the person on the dynamic exercise. As a measure of the cardiovascular system of the person (to load and after the load) used quasi-attractor motion of the state vector of the system in the two-dimensional phase space of states. Within the framework of the theory of chaos and self-organization may determine the parameters of the spacecraft for individual subjects and their groups to compare their chaotic dynamics in time or in the phase space of states.

An improved chaotic hybrid differential evolution for the short-term hydrothermal scheduling problem considering practical constraints

Short-term hydrothermal scheduling (STHTS) is a non-linear and complex optimization problem with a set of operational hydraulic and thermal constraints. Earlier, this problem has been addressed by several classical techniques; however, due to limitations such as non-linearity and non-convexity in cost curves, artificial intelligence tools based techniques are being used to solve the STHTS problem. In this paper an improved chaotic hybrid differential evolution (ICHDE) algorithm is proposed to find an optimal solution to this problem taking into account practical constraints. A self-adjusted parameter setting is obtained in differential evolution (DE) with the application of chaos theory, and a chaotic hybridized local search mechanism is embedded in DE to effectively prevent it from premature convergence. Furthermore, heuristic constraint handling techniques without any penalty factor setting are adopted to handle the complex hydraulic and thermal constraints. The superiority and effectiveness of the developed methodology are evaluated by its application in two illustrated hydrothermal test systems taken from the literature. The transmission line losses, prohibited discharge zones of hydel plants, and ramp rate limits of thermal plants are also taken into account. The simulation results reveal that the proposed technique is competent to produce an encouraging solution as compared with other recently established evolutionary approaches.