Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 100

Search results for: chaos

100 On Deterministic Chaos: Disclosing the Missing Mathematics from the Lorenz-Haken Equations

Authors: Meziane Belkacem


We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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99 Main Chaos-Based Image Encryption Algorithm

Authors: Ibtissem Talbi


During the last decade, a variety of chaos-based cryptosystems have been investigated. Most of them are based on the structure of Fridrich, which is based on the traditional confusion-diffusion architecture proposed by Shannon. Compared with traditional cryptosystems (DES, 3DES, AES, etc.), the chaos-based cryptosystems are more flexible, more modular and easier to be implemented, which make them suitable for large scale-data encyption, such as images and videos. The heart of any chaos-based cryptosystem is the chaotic generator and so, a part of the efficiency (robustness, speed) of the system depends greatly on it. In this talk, we give an overview of the state of the art of chaos-based block ciphers and we describe some of our schemes already proposed. Also we will focus on the essential characteristics of the digital chaotic generator, The needed performance of a chaos-based block cipher in terms of security level and speed of calculus depends on the considered application. There is a compromise between the security and the speed of the calculation. The security of these block block ciphers will be analyzed.

Keywords: chaos-based cryptosystems, chaotic generator, security analysis, structure of Fridrich

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98 A Novel Parametric Chaos-Based Switching System PCSS for Image Encryption

Authors: Mohamed Salah Azzaz, Camel Tanougast, Tarek Hadjem


In this paper, a new low-cost image encryption technique is proposed and analyzed. The developed chaos-based key generator provides complex behavior and can change it automatically via a random-like switching rule. The designed encryption scheme is called PCSS (Parametric Chaos-based Switching System). The performances of this technique were evaluated in terms of data security and privacy. Simulation results have shown the effectiveness of this technique, and it can thereafter, ready for a hardware implementation.

Keywords: chaos, encryption, security, image

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97 An Efficient Discrete Chaos in Generalized Logistic Maps with Applications in Image Encryption

Authors: Ashish Ashish


In the last few decades, the discrete chaos of difference equations has gained a massive attention of academicians and scholars due to its tremendous applications in each and every branch of science, such as cryptography, traffic control models, secure communications, weather forecasting, and engineering. In this article, a generalized logistic discrete map is established and discrete chaos is reported through period doubling bifurcation, period three orbit and Lyapunov exponent. It is interesting to see that the generalized logistic map exhibits superior chaos due to the presence of an extra degree of freedom of an ordered parameter. The period doubling bifurcation and Lyapunov exponent are demonstrated for some particular values of parameter and the discrete chaos is determined in the sense of Devaney's definition of chaos theoretically as well as numerically. Moreover, the study discusses an extended chaos based image encryption and decryption scheme in cryptography using this novel system. Surprisingly, a larger key space for coding and more sensitive dependence on initial conditions are examined for encryption and decryption of text messages, images and videos which secure the system strongly from external cyber attacks, coding attacks, statistic attacks and differential attacks.

Keywords: chaos, period-doubling, logistic map, Lyapunov exponent, image encryption

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96 Whether Chaos Theory Could Reconstruct the Ancient Societies

Authors: Zahra Kouzehgari


Since the early emergence of chaos theory in the 1970s in mathematics and physical science, it has increasingly been developed and adapted in social sciences as well. The non-linear and dynamic characteristics of the theory make it a useful conceptual framework to interpret the complex social systems behavior. Regarding chaotic approach principals, sensitivity to initial conditions, dynamic adoption, strange attractors and unpredictability this paper aims to examine whether chaos approach could interpret the ancient social changes. To do this, at first, a brief history of the chaos theory, its development and application in social science as well as the principals making the theory, then its application in archaeological since has been reviewed. The study demonstrates that although based on existing archaeological records reconstruct the whole social system of the human past, the non-linear approaches in studying social complex systems would be of a great help in finding general order of the ancient societies and would enable us to shed light on some of the social phenomena in the human history or to make sense of them.

Keywords: archaeology, non-linear approach, chaos theory, ancient social systems

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95 Chaotic Dynamics of Cost Overruns in Oil and Gas Megaprojects: A Review

Authors: O. J. Olaniran, P. E. D. Love, D. J. Edwards, O. Olatunji, J. Matthews


Cost overruns are a persistent problem in oil and gas megaprojects. Whilst the extant literature is filled with studies on incidents and causes of cost overruns, underlying theories to explain their emergence in oil and gas megaprojects are few. Yet, a way to contain the syndrome of cost overruns is to understand the bases of ‘how and why’ they occur. Such knowledge will also help to develop pragmatic techniques for better overall management of oil and gas megaprojects. The aim of this paper is to explain the development of cost overruns in hydrocarbon megaprojects through the perspective of chaos theory. The underlying principles of chaos theory and its implications for cost overruns are examined and practical recommendations proposed. In addition, directions for future research in this fertile area provided.

Keywords: chaos theory, oil and gas, cost overruns, megaprojects

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94 Solving SPDEs by Least Squares Method

Authors: Hassan Manouzi


We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method

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93 Small Entrepreneurs as Creators of Chaos: Increasing Returns Requires Scaling

Authors: M. B. Neace, Xin GAo


Small entrepreneurs are ubiquitous. Regardless of location their success depends on several behavioral characteristics and several market conditions. In this concept paper, we extend this paradigm to include elements from the science of chaos. Our observations, research findings, literature search and intuition lead us to the proposition that all entrepreneurs seek increasing returns, as did the many small entrepreneurs we have interviewed over the years. There will be a few whose initial perturbations may create tsunami-like waves of increasing returns over time resulting in very large market consequences–the butterfly impact. When small entrepreneurs perturb the market-place and their initial efforts take root a series of phase-space transitions begin to occur. They sustain the stream of increasing returns by scaling up. Chaos theory contributes to our understanding of this phenomenon. Sustaining and nourishing increasing returns of small entrepreneurs as complex adaptive systems requires scaling. In this paper we focus on the most critical element of the small entrepreneur scaling process–the mindset of the owner-operator.

Keywords: entrepreneur, increasing returns, scaling, chaos

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92 Melnikov Analysis for the Chaos of the Nonlocal Nanobeam Resting on Fractional-Order Softening Nonlinear Viscoelastic Foundations

Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane


In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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91 Chaotic Analysis of Acid Rains with Times Series of pH Degree, Nitrate and Sulphate Concentration on Wet Samples

Authors: Aysegul Sener, Gonca Tuncel Memis, Mirac Kamislioglu


Chaos theory is one of the new paradigms of science since the last century. After determining chaos in the weather systems by Edward Lorenz the popularity of the theory was increased. Chaos is observed in many natural systems and studies continue to defect chaos to other natural systems. Acid rain is one of the environmental problems that have negative effects on environment and acid rains values are monitored continuously. In this study, we aim that analyze the chaotic behavior of acid rains in Turkey with the chaotic defecting approaches. The data of pH degree of rain waters, concentration of sulfate and nitrate data of wet rain water samples in the rain collecting stations which are located in different regions of Turkey are provided by Turkish State Meteorology Service. Lyapunov exponents, reconstruction of the phase space, power spectrums are used in this study to determine and predict the chaotic behaviors of acid rains. As a result of the analysis it is found that acid rain time series have positive Lyapunov exponents and wide power spectrums and chaotic behavior is observed in the acid rain time series.

Keywords: acid rains, chaos, chaotic analysis, Lypapunov exponents

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90 Design of Chaos Algorithm Based Optimal PID Controller for SVC

Authors: Saeid Jalilzadeh


SVC is one of the most significant devices in FACTS technology which is used in parallel compensation, enhancing the transient stability, limiting the low frequency oscillations and etc. designing a proper controller is effective in operation of svc. In this paper the equations that describe the proposed system have been linearized and then the optimum PID controller has been designed for svc which its optimal coefficients have been earned by chaos algorithm. Quick damping of oscillations of generator is the aim of designing of optimum PID controller for svc whether the input power of generator has been changed suddenly. The system with proposed controller has been simulated for a special disturbance and the dynamic responses of generator have been presented. The simulation results showed that a system composed with proposed controller has suitable operation in fast damping of oscillations of generator.

Keywords: chaos, PID controller, SVC, frequency oscillation

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89 Drift-Wave Turbulence in a Tokamak Edge Plasma

Authors: S. Belgherras Bekkouche, T. Benouaz, S. M. A. Bekkouche


Tokamak plasma is far from having a stable background. The study of turbulent transport is an important part of the current research and advanced scenarios were devised to minimize it. To do this, we used a three-wave interaction model which allows to investigate the occurrence drift-wave turbulence driven by pressure gradients in the edge plasma of a tokamak. In order to simulate the energy redistribution among different modes, the growth/decay rates for the three waves was added. After a numerical simulation, we can determine certain aspects of the temporal dynamics exhibited by the model. Indeed for a wide range of the wave decay rate, an intermittent transition from periodic behavior to chaos is observed. Then, a control strategy of chaos was introduced with the aim of reducing or eliminating the weak turbulence.

Keywords: wave interaction, plasma drift waves, wave turbulence, tokamak, edge plasma, chaos

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88 Polynomial Chaos Expansion Combined with Exponential Spline for Singularly Perturbed Boundary Value Problems with Random Parameter

Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy


So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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87 Identifying Chaotic Architecture: Origins of Nonlinear Design Theory

Authors: Mohammadsadegh Zanganehfar


Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

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86 Chaotic Control, Masking and Secure Communication Approach of Supply Chain Attractor

Authors: Unal Atakan Kahraman, Yilmaz Uyaroğlu


The chaotic signals generated by chaotic systems have some properties such as randomness, complexity and sensitive dependence on initial conditions, which make them particularly suitable for secure communications. Since the 1990s, the problem of secure communication, based on chaos synchronization, has been thoroughly investigated and many methods, for instance, robust and adaptive control approaches, have been proposed to realize the chaos synchronization. In this paper, an improved secure communication model is proposed based on control of supply chain management system. Control and masking communication simulation results are used to visualize the effectiveness of chaotic supply chain system also performed on the application of secure communication to the chaotic system. So, we discover the secure phenomenon of chaos-amplification in supply chain system

Keywords: chaotic analyze, control, secure communication, supply chain attractor

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85 Complexity in a Leslie-Gower Delayed Prey-Predator Model

Authors: Anuraj Singh


The complex dynamics is explored in a prey predator system with multiple delays. The predator dynamics is governed by Leslie-Gower scheme. The existence of periodic solutions via Hopf bifurcation with respect to delay parameters is established. To substantiate analytical findings, numerical simulations are performed. The system shows rich dynamic behavior including chaos and limit cycles.

Keywords: chaos, Hopf bifurcation, stability, time delay

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84 Feigenbaum Universality, Chaos and Fractal Dimensions in Discrete Dynamical Systems

Authors: T. K. Dutta, K. K. Das, N. Dutta


The salient feature of this paper is primarily concerned with Ricker’s population model: f(x)=x e^(r(1-x/k)), where r is the control parameter and k is the carrying capacity, and some fruitful results are obtained with the following objectives: 1) Determination of bifurcation values leading to a chaotic region, 2) Development of Statistical Methods and Analysis required for the measure of Fractal dimensions, 3) Calculation of various fractal dimensions. These results also help that the invariant probability distribution on the attractor, when it exists, provides detailed information about the long-term behavior of a dynamical system. At the end, some open problems are posed for further research.

Keywords: Feigenbaum universality, chaos, Lyapunov exponent, fractal dimensions

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83 A User Interface for Easiest Way Image Encryption with Chaos

Authors: D. López-Mancilla, J. M. Roblero-Villa


Since 1990, the research on chaotic dynamics has received considerable attention, particularly in light of potential applications of this phenomenon in secure communications. Data encryption using chaotic systems was reported in the 90's as a new approach for signal encoding that differs from the conventional methods that use numerical algorithms as the encryption key. The algorithms for image encryption have received a lot of attention because of the need to find security on image transmission in real time over the internet and wireless networks. Known algorithms for image encryption, like the standard of data encryption (DES), have the drawback of low level of efficiency when the image is large. The encrypting based on chaos proposes a new and efficient way to get a fast and highly secure image encryption. In this work, a user interface for image encryption and a novel and easiest way to encrypt images using chaos are presented. The main idea is to reshape any image into a n-dimensional vector and combine it with vector extracted from a chaotic system, in such a way that the vector image can be hidden within the chaotic vector. Once this is done, an array is formed with the original dimensions of the image and turns again. An analysis of the security of encryption from the images using statistical analysis is made and is used a stage of optimization for image encryption security and, at the same time, the image can be accurately recovered. The user interface uses the algorithms designed for the encryption of images, allowing you to read an image from the hard drive or another external device. The user interface, encrypt the image allowing three modes of encryption. These modes are given by three different chaotic systems that the user can choose. Once encrypted image, is possible to observe the safety analysis and save it on the hard disk. The main results of this study show that this simple method of encryption, using the optimization stage, allows an encryption security, competitive with complicated encryption methods used in other works. In addition, the user interface allows encrypting image with chaos, and to submit it through any public communication channel, including internet.

Keywords: image encryption, chaos, secure communications, user interface

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82 Detection of Chaos in General Parametric Model of Infectious Disease

Authors: Javad Khaligh, Aghileh Heydari, Ali Akbar Heydari


Mathematical epidemiological models for the spread of disease through a population are used to predict the prevalence of a disease or to study the impacts of treatment or prevention measures. Initial conditions for these models are measured from statistical data collected from a population since these initial conditions can never be exact, the presence of chaos in mathematical models has serious implications for the accuracy of the models as well as how epidemiologists interpret their findings. This paper confirms the chaotic behavior of a model for dengue fever and SI by investigating sensitive dependence, bifurcation, and 0-1 test under a variety of initial conditions.

Keywords: epidemiological models, SEIR disease model, bifurcation, chaotic behavior, 0-1 test

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81 Solving Stochastic Eigenvalue Problem of Wick Type

Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati


In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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80 Control of Chaotic Behaviour in Parallel-Connected DC-DC Buck-Boost Converters

Authors: Ammar Nimer Natsheh


Chaos control is used to design a controller that is able to eliminate the chaotic behaviour of nonlinear dynamic systems that experience such phenomena. The paper describes the control of the bifurcation behaviour of a parallel-connected DC-DC buck-boost converter used to provide an interface between energy storage batteries and photovoltaic (PV) arrays as renewable energy sources. The paper presents a delayed feedback control scheme in a module converter comprises two identical buck-boost circuits and operates in the continuous-current conduction mode (CCM). MATLAB/SIMULINK simulation results show the effectiveness and robustness of the scheme.

Keywords: chaos, bifurcation, DC-DC Buck-Boost Converter, Delayed Feedback Control

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79 Container Chaos: The Impact of a Casual Game on Learning and Behavior

Authors: Lori L. Scarlatos, Ryan Courtney


This paper explores the impact that playing a casual game can have on a player's learning and subsequent behavior. A casual mobile game, Container Chaos, was created to teach undergraduate students about the carbon footprint of various disposable beverage containers. Learning was tested with a short quiz, and behavior was tested by observing which beverage containers players choose when offered a drink and a snack. The game was tested multiple times, under a variety of different circumstances. Findings of these tests indicate that, with extended play over time, players can learn new information and sometimes even change their behavior as a result. This has implications for how other casual games can be used to teach concepts and possibly modify behavior.

Keywords: behavior, carbon footprint, casual games, environmental impact, material sciences

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78 For a Poetic Clinic: Experimentations at Risk on the Images in Performances

Authors: Juliana Bom-Tempo


The proposed composition occurs between images, performances, clinics and philosophies. For this enterprise we depart for what is not known beforehand, so with a question as a compass: "would it be in the creation, production and implementation of images in a performance a 'when' for the event of a poetic clinic?” In light of this, there are, in order to think a 'when' of the event of a poetic clinic, images in performances created, produced and executed in partnerships with the author of this text. Faced with this composition, we built four indicators to find spatiotemporal coordinates that would spot that "when", namely: risk zones; the mobilizations of the signs; the figuring of the flesh and an education of the affections. We dealt with the images in performances; Crútero; Flesh; Karyogamy and the risk of abortion; Egg white; Egg-mouth; Islands, threads, words ... germs; Egg-Mouth-Debris, taken as case studies, by engendering risks areas to promote individuations, which never actualize thoroughly, thus always something of pre-individual and also individuating a environment; by mobilizing the signs territorialized by the ordinary, causing them to vary the language and the words of order dictated by the everyday in other compositions of sense, other machinations; by generating a figure of flesh, disarranging the bodies, isolating them in the production of a ground force that causes the body to leak out and undo the functionalities of the organs; and, finally, by producing an education of affections, by placing the perceptions in becoming and disconnecting the visible in the production of small deserts that call for the creation of a people yet to come. The performance is processed as a problematizing of the images fixed by the ordinary, producing gestures that precipitate the individuation of images in performance, strange to the configurations that gather bodies and spaces in what we call common. Lawrence proposes to think of "people" who continually use umbrellas to protect themselves from chaos. These have the function of wrapping up the chaos in visions that create houses, forms and stabilities; they paint a sky at the bottom of the umbrella, where people march and die. A chaos, where people live and wither. Pierce the umbrella for a desire of chaos; a poet puts himself as an enemy of the convention, to be able to have an image of chaos and a little sun that burns his skin. The images in performances presented, thereby, were moving in search for the power of producing a spatio-temporal "when" putting the territories in risk areas, mobilizing the signs that format the day-to-day, opening the bodies to a disorganization and the production of an education of affections for the event of a poetic clinic.

Keywords: Experimentations , Images in Performances, Poetic Clinic, Risk

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77 Analysis of Cardiac Health Using Chaotic Theory

Authors: Chandra Mukherjee


The prevalent knowledge of the biological systems is based on the standard scientific perception of natural equilibrium, determination and predictability. Recently, a rethinking of concepts was presented and a new scientific perspective emerged that involves complexity theory with deterministic chaos theory, nonlinear dynamics and theory of fractals. The unpredictability of the chaotic processes probably would change our understanding of diseases and their management. The mathematical definition of chaos is defined by deterministic behavior with irregular patterns that obey mathematical equations which are critically dependent on initial conditions. The chaos theory is the branch of sciences with an interest in nonlinear dynamics, fractals, bifurcations, periodic oscillations and complexity. Recently, the biomedical interest for this scientific field made these mathematical concepts available to medical researchers and practitioners. Any biological network system is considered to have a nominal state, which is recognized as a homeostatic state. In reality, the different physiological systems are not under normal conditions in a stable state of homeostatic balance, but they are in a dynamically stable state with a chaotic behavior and complexity. Biological systems like heart rhythm and brain electrical activity are dynamical systems that can be classified as chaotic systems with sensitive dependence on initial conditions. In biological systems, the state of a disease is characterized by a loss of the complexity and chaotic behavior, and by the presence of pathological periodicity and regulatory behavior. The failure or the collapse of nonlinear dynamics is an indication of disease rather than a characteristic of health.

Keywords: HRV, HRVI, LF, HF, DII

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76 Analysis of Nonlinear Bertrand Duopoly Game with Heterogeneous Players

Authors: Jixiang Zhang


A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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75 Dynamic of Nonlinear Duopoly Game with Heterogeneous Players

Authors: Jixiang Zhang, Yanhua Wang


A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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74 Quantum Statistical Machine Learning and Quantum Time Series

Authors: Omar Alzeley, Sergey Utev


Minimizing a constrained multivariate function is the fundamental of Machine learning, and these algorithms are at the core of data mining and data visualization techniques. The decision function that maps input points to output points is based on the result of optimization. This optimization is the central of learning theory. One approach to complex systems where the dynamics of the system is inferred by a statistical analysis of the fluctuations in time of some associated observable is time series analysis. The purpose of this paper is a mathematical transition from the autoregressive model of classical time series to the matrix formalization of quantum theory. Firstly, we have proposed a quantum time series model (QTS). Although Hamiltonian technique becomes an established tool to detect a deterministic chaos, other approaches emerge. The quantum probabilistic technique is used to motivate the construction of our QTS model. The QTS model resembles the quantum dynamic model which was applied to financial data. Secondly, various statistical methods, including machine learning algorithms such as the Kalman filter algorithm, are applied to estimate and analyses the unknown parameters of the model. Finally, simulation techniques such as Markov chain Monte Carlo have been used to support our investigations. The proposed model has been examined by using real and simulated data. We establish the relation between quantum statistical machine and quantum time series via random matrix theory. It is interesting to note that the primary focus of the application of QTS in the field of quantum chaos was to find a model that explain chaotic behaviour. Maybe this model will reveal another insight into quantum chaos.

Keywords: machine learning, simulation techniques, quantum probability, tensor product, time series

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73 Chaos Cryptography in Cloud Architectures with Lower Latency

Authors: Mohammad A. Alia


With the rapid evolution of the internet applications, cloud computing becomes one of today’s hottest research areas due to its ability to reduce costs associated with computing. Cloud is, therefore, increasing flexibility and scalability for computing services in the internet. Cloud computing is Internet based computing due to shared resources and information which are dynamically delivered to consumers. As cloud computing share resources via the open network, hence cloud outsourcing is vulnerable to attack. Therefore, this paper will explore data security of cloud computing by implementing chaotic cryptography. The proposal scenario develops a problem transformation technique that enables customers to secretly transform their information. This work proposes the chaotic cryptographic algorithms have been applied to enhance the security of the cloud computing accessibility. However, the proposed scenario is secure, easy and straightforward process. The chaotic encryption and digital signature systems ensure the security of the proposed scenario. Though, the choice of the key size becomes crucial to prevent a brute force attack.

Keywords: chaos, cloud computing, security, cryptography

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72 Quantum Localization of Vibrational Mirror in Cavity Optomechanics

Authors: Madiha Tariq, Hena Rabbani


Recently, cavity-optomechanics becomes an extensive research field that has manipulated the mechanical effects of light for coupling of the optical field with other physical objects specifically with regards to dynamical localization. We investigate the dynamical localization (both in momentum and position space) for a vibrational mirror in a Fabry-Pérot cavity driven by a single mode optical field and a transverse probe field. The weak probe field phenomenon results in classical chaos in phase space and spatio temporal dynamics in position |ψ(x)²| and momentum space |ψ(p)²| versus time show quantum localization in both momentum and position space. Also, we discuss the parametric dependencies of dynamical localization for a designated set of parameters to be experimentally feasible. Our work opens an avenue to manipulate the other optical phenomena and applicability of proposed work can be prolonged to turn-able laser sources in the future.

Keywords: dynamical localization, cavity optomechanics, Hamiltonian chaos, probe field

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71 Implementation in Python of a Method to Transform One-Dimensional Signals in Graphs

Authors: Luis Andrey Fajardo Fajardo


We are immersed in complex systems. The human brain, the galaxies, the snowflakes are examples of complex systems. An area of interest in Complex systems is the chaos theory. This revolutionary field of science presents different ways of study than determinism and reductionism. Here is where in junction with the Nonlinear DSP, chaos theory offer valuable techniques that establish a link between time series and complex theory in terms of complex networks, so that, the study of signals can be explored from the graph theory. Recently, some people had purposed a method to transform time series in graphs, but no one had developed a suitable implementation in Python with signals extracted from Chaotic Systems or Complex systems. That’s why the implementation in Python of an existing method to transform one dimensional chaotic signals from time domain to graph domain and some measures that may reveal information not extracted in the time domain is proposed.

Keywords: Python, complex systems, graph theory, dynamical systems

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