Search results for: chaotic approach

Authors: Harsh Vikram Singh, Ankur Rai, Anand Mohan

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In this paper, we propose secure and robust data hiding algorithm based on DCT by Arnold transform and chaotic sequence. The watermark image is scrambled by Arnold cat map to increases its security and then the chaotic map is used for watermark signal spread in middle band of DCT coefficients of the cover image The chaotic map can be used as pseudo-random generator for digital data hiding, to increase security and robustness .Performance evaluation for robustness and imperceptibility of proposed algorithm has been made using bit error rate (BER), normalized correlation (NC), and peak signal to noise ratio (PSNR) value for different watermark and cover images such as Lena, Girl, Tank images and gain factor .We use a binary logo image and text image as watermark. The experimental results demonstrate that the proposed algorithm achieves higher security and robustness against JPEG compression as well as other attacks such as addition of noise, low pass filtering and cropping attacks compared to other existing algorithm using DCT coefficients. Moreover, to recover watermarks in proposed algorithm, there is no need to original cover image.

Keywords: data hiding, watermarking, DCT, chaotic sequence, arnold transforms

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Authors: Chandra Mukherjee

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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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Authors: Yi-Fei Yang, Nai-Bao He, Shao-Bang Xing

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This study investigates the permanent magnet synchronous linear motor (PMSLM) chaotic motion under the specific physical parameters, the stability and the security of motor-driven system will be unavoidably influenced. Therefore, it is really necessary to investigate the methods of controlling or suppressing chaos in PMSLM. Firstly, we derive a chaotic model of PMSLM in the closed-loop system. Secondly, in order to realize the local asymptotic stabilization of the mechanical subsystem and the global stabilization of the motor-driven system including electrical subsystem, we propose an improved uniting control lyapunov functions by introducing backstepping approach. Finally, an illustrated example is also given to show the electiveness of the obtained results.

Keywords: linear motor, lyapunov functions, chao control, hybrid controller

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Authors: Mohammadsadegh Zanganehfar

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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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Authors: Mohammad A. Alia

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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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Authors: Ibtissem Talbi

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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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Authors: Yang Yi-Fei, Luo Min-Zhou, Zhang Fu-Chun, He Nai-Bao, Xing Shao-Bang

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This paper presents an electromagnetic finite element model of permanent magnet synchronous linear motor and distortion rate of the air gap flux density waveform is analyzed in detail. By designing the sample space of the parameters, nonlinear regression modeling of the orthogonal experimental design is introduced. We put forward for possible air gap flux density waveform sine electromagnetic scheme. Parameters optimization of the permanent magnet synchronous linear motor is also introduced which is based on chaotic search and adaptation function. Simulation results prove that the pole shifting does not affect the motor back electromotive symmetry based on the structural parameters, it provides a novel way for the optimum design of permanent magnet synchronous linear motor and other engineering.

Keywords: permanent magnet synchronous linear motor, finite element analysis, chaotic search, optimization design

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Authors: R. M. López-Gutiérrez, L. Cardoza-Avendaño, H. Cervantes-de Ávila, J. A. Michel-Macarty, C. Cruz-Hernández, A. Arellano-Delgado, R. Carmona-Rodríguez

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In this paper, synchronization of multiple chaotic semiconductor lasers is achieved by appealing to complex system theory. In particular, we consider dynamical networks composed by semiconductor laser, as interconnected nodes, where the interaction in the networks are defined by coupling the first state of each node. An interesting case is synchronized with master-slave configuration in star topology. Nodes of these networks are modeled for the laser and simulated by Matlab. These results are applicable to private communication.

Keywords: chaotic laser, network, star topology, synchronization

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Authors: Shaban Aly, Ali Al-Qahtani, Houari B. Khenous

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Synchronization is an important phenomenon commonly observed in nature. A system of periodically forced complex Duffings oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using impulsive synchronization techniques. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Keywords: complex nonlinear oscillators, impulsive synchronization, chaotic systems, global exponential synchronization

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Authors: Roger Yu

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A numerical scheme has been developed to solve wave equations for chaotic systems such as stadium-shaped cavity. The same numerical method can also be used for finding wave properties of rectangle cavities with randomly placed obstacles. About 30k eigenvalues have been obtained accurately on a normal circumstance. For comparison, we also initiated an experimental study which determines both eigenfrequencies and eigenfunctions of a stadium-shaped cavity using pulse and normal mode analyzing techniques. The acoustic cavity was made adjustable so that the transition from nonchaotic (circle) to chaotic (stadium) waves can be investigated.

Keywords: quantum dot, chaos, numerical method, eigenvalues

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Authors: Ramonika Sengupta, Stuti Kachhwaha, Asha Adhiya, K. Satya Raja Sekhar, Rajwinder Kaur

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Numerous efforts have been done in the past decade to develop the methods of secure communication that are free from interception and eavesdropping. In fiber optic communication, chaotic optical carrier signals are used for data encryption in secure data transmission. Mach-Zehnder Modulators (MZM) are the key components for generating the chaotic signals to be used as optical carriers. This paper presents the dynamics of a lithium niobate MZM modulator under various biasing conditions. The chaotic fluctuations of the intensity of a laser diode have been generated using the electro-optic MZM modulator operating in a highly nonlinear regime. The modulator is driven in closed loop by its own output at an earlier time. When used as an electro-optic oscillator employing delayed feedback, the MZM displays a wide range of output waveforms of varying complexity. The dynamical behavior of the system ranges from periodic to nonlinear oscillations. The nonlinearity displayed by the system is reproducible and is easily controllable. In this paper, we demonstrate a wide variety of optical signals generated by MZM using easily controllable device parameters in both open and close loop bias conditions.

Keywords: chaotic carrier, fiber optic communication, Mach-Zehnder modulator, secure data transmission

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Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam

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In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Lyapunov stability, synchronization, chaos, optimal control, adaptive control

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Authors: Yuzuru Mitsui, Takashi Ikegami

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The exponents of Taylor’s law in deterministic chaotic systems are computed, and their meanings are intensively discussed. Taylor’s law is the scaling relationship between the mean and variance (in both space and time) of population abundance, and this law is known to hold in a variety of ecological time series. The exponents found in the temporal Taylor’s law are different from those of the spatial Taylor’s law. The temporal Taylor’s law is calculated on the time series from the same locations (or the same initial states) of different temporal phases. However, with the spatial Taylor’s law, the mean and variance are calculated from the same temporal phase sampled from different places. Most previous studies were done with stochastic models, but we computed the temporal and spatial Taylor’s law in deterministic systems. The temporal Taylor’s law evaluated using the same initial state, and the spatial Taylor’s law was evaluated using the ensemble average and variance. There were two main discoveries from this work. First, it is often stated that deterministic systems tend to have the value two for Taylor’s exponent. However, most of the calculated exponents here were not two. Second, we investigated the relationships between chaotic features measured by the Lyapunov exponent, the correlation dimension, and other indexes with Taylor’s exponents. No strong correlations were found; however, there is some relationship in the same model, but with different parameter values, and we will discuss the meaning of those results at the end of this paper.

Keywords: chaos, density effect, population dynamics, Taylor’s law

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Authors: Javad Khaligh, Aghileh Heydari, Ali Akbar Heydari

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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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Authors: Ammar Nimer Natsheh

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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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Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

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Authors: Zahra Kouzehgari

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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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Authors: George Mahalu

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The Chua diode has been configured over time in various ways, using electronic structures like operational amplifiers (AOs) or devices with gas or semiconductors. When discussing the use of semiconductor devices, tunnel diodes (Esaki diodes) are most often considered, and more recently, transistorized configurations such as lambda diodes. The paperwork proposed here uses in the modeling a lambda diode type configuration consisting of two junction field effect transistors (JFET). The original scheme is created in the MULTISIM electronic simulation environment and is analyzed in order to identify the conditions for the appearance of evolutionary unpredictability specific to nonlinear dynamic systems with chaos-induced behavior. The chaotic deterministic oscillator is one autonomous type, a fact that places it in the class of Chua’s type oscillators, the only significant and most important difference being the presence of a nonlinear device like the one mentioned structure above. The chaotic behavior is identified both by means of strange attractor-type trajectories and visible during the simulation and by highlighting the hypersensitivity of the system to small variations of one of the input parameters. The results obtained through simulation and the conclusions drawn are useful in the further research of ways to implement such constructive electronic solutions in theoretical and practical applications related to modern small signal amplification structures, to systems for encoding and decoding messages through various modern ways of communication, as well as new structures that can be imagined both in modern neural networks and in those for the physical implementation of some requirements imposed by current research with the aim of obtaining practically usable solutions in quantum computing and quantum computers.

Keywords: chua, diode, memristor, chaos

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Authors: D. M. S. Bandara, Yunqi Lei, Ye Luo

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Fingerprints are suitable as long-term markers of human identity since they provide detailed and unique individual features which are difficult to alter and durable over life time. In this paper, we propose an algorithm to encrypt and decrypt fingerprint images by using a specially designed Elliptic Curve Cryptography (ECC) procedure based on block ciphers. In addition, to increase the confusing effect of fingerprint encryption, we also utilize a chaotic-behaved method called Arnold Cat Map (ACM) for a 2D scrambling of pixel locations in our method. Experimental results are carried out with various types of efficiency and security analyses. As a result, we demonstrate that the proposed fingerprint encryption/decryption algorithm is advantageous in several different aspects including efficiency, security and flexibility. In particular, using this algorithm, we achieve a margin of about 0.1% in the test of Number of Pixel Changing Rate (NPCR) values comparing to the-state-of-the-art performances.

Keywords: arnold cat map, biometric encryption, block cipher, elliptic curve cryptography, fingerprint encryption, Koblitz’s encoding

Procedia PDF Downloads 172

Authors: George Mahalu

Abstract:

The Chua diode has been configured over time in various ways, using electronic structures like as operational amplifiers (OAs) or devices with gas or semiconductors. When discussing the use of semiconductor devices, tunnel diodes (Esaki diodes) are most often considered, and more recently, transistorized configurations such as lambda diodes. The paper-work proposed here uses in the modeling a lambda diode type configuration consisting of two Junction Field Effect Transistors (JFET). The original scheme is created in the MULTISIM electronic simulation environment and is analyzed in order to identify the conditions for the appearance of evolutionary unpredictability specific to nonlinear dynamic systems with chaos-induced behavior. The chaotic deterministic oscillator is one autonomous type, a fact that places it in the class of Chua’s type oscillators, the only significant and most important difference being the presence of a nonlinear device like the one mentioned structure above. The chaotic behavior is identified both by means of strange attractor-type trajectories and visible during the simulation and by highlighting the hypersensitivity of the system to small variations of one of the input parameters. The results obtained through simulation and the conclusions drawn are useful in the further research of ways to implement such constructive electronic solutions in theoretical and practical applications related to modern small signal amplification structures, to systems for encoding and decoding messages through various modern ways of communication, as well as new structures that can be imagined both in modern neural networks and in those for the physical implementation of some requirements imposed by current research with the aim of obtaining practically usable solutions in quantum computing and quantum computers.

Keywords: chaos, lambda diode, strange attractor, nonlinear system

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Authors: Sarah Eldefrawi, Maike Didero

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In Egypt, residents’ urban interventions (colloquially named A’hali’s interventions) are always tackled by government, scholars, and media as an encroachment (taeadiyat), chaotic (a’shwa’i) or informal (gheir mokanan) practices. This paper argues that those interventions cannot be simply described as an encroachment on public space or chaotic behaviour. We claim here that they are relevant to traditional governing methods (‘Urf) that were governing Arab cities for many decades. Through an in-depth field study conducted in a real estate public housing project in the city of Giza called 'Masaken El-Barageel', we traced the urban transformations demonstrated in private and public spaces. To understand those transformations, we used wide-range of qualitative research methods such as semi-guided and informal interviews, observations and mapping of the built environment and the newly added interventions. This study was as well strengthened through the contributions of the author in studying nine sectors emerging by Ahali in six districts in Great Cairo. The results of this study indicate that a culturally and socially sensitive framework has to be related to the individual actions toward the spatial and social structures as well as to culturally transmitted views and meanings connected with 'Urf'. The study could trace three crucial principals in ‘urf that influenced these interventions; the eliminating of harm (Al-Marafiq wa Man’ al-Darar), the appropriation of space (Haqq el-Intefa’) and public interest (maslaha a’ma). Our findings open the discussion for the (il) legitimate of a’hali governing methods in contemporary cities.

Keywords: Urf, urban governance, public space, public housing, encroachments, chaotic, Egyptian cities

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Authors: Luis Andrey Fajardo Fajardo

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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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Authors: Sina Modares Ahmadi, Mohamad Reza Ghazavi, Mandana Sheikhzad

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Squeeze film damper systems (SFD) are often used in machines with high rotational speed to reduce non-periodic behavior by creating external damping. These types of systems are frequently used in aircraft gas turbine engines. There are some structural parameters which are of great importance in designing these kinds of systems, such as oil film thickness, C, and outer race mass, mo. Moreover, there is a crucial parameter associated with manufacturing process, under the title of waviness. Geometric imperfections are often called waviness if its wavelength is much longer than Hertzian contact width which is a considerable source of vibration in ball bearings. In this paper, a system of a flexible rotor and two ball bearings with floating ring squeeze film dampers and consideration of waviness has been modeled and solved by a numerical integration method, namely Runge-Kutta method to investigate the dynamic response of the system. The results show that by increasing the number of wave lobes, which is due to inappropriate manufacturing, non- periodic and chaotic behavior increases. This result reveals the importance of manufacturing accuracy. Moreover, as long as C< 1.5×10-4 m, by increasing the oil film thickness, unwanted vibrations and non-periodic behavior of the system have been reduced, On the other hand, when C>1.5×10-4 m, increasing the outer oil film thickness results in the increasing chaotic and non-periodic responses. This result shows that although the presence of oil film results in reduction the non-periodic and chaotic behaviors, but the oil film has an optimal thickness. In addition, with increasing mo, the disc displacement amplitude increases. This result reveals the importance of utilizing light materials in manufacturing the squeeze film dampers.

Keywords: squeeze-film damper, waviness, ball bearing, bifurcation

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Authors: Arijit Basuray

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It is well known that if an electrical insulation system is stressed under high voltage then discharge may occur in various form and if the system is made of composite dielectric having interfaces of materials having different dielectric constant discharge may occur due to gross mismatch of dielectric constant causing intense local field in the interfaces. Here author has studied, firstly, behavior of discharges in gaseous dielectric circuit under AC and DC voltages. A gaseous dielectric circuit is made such that a pair of electrode of typical geometry is used to make the discharges occur under application of AC and DC voltages. Later on, composite insulation system with air gap is also studied. Discharge response of the dielectric circuit is measured across a typically designed impedance. The time evolution of the discharge characteristics showed some interesting chaotic behavior. Author here proposed some analysis of such behavior of the discharge pattern and discussed about the possibility of presence of such discharge circuit in lumped electric circuit.

Keywords: electrical insulation system, EIS, composite dielectric, discharge, chaos

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Authors: T. Ganesan, M. S. Aris, I. Elamvazuthi, Momen Kamal Tageldeen

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Terms set in power purchase agreements (PPA) challenge power utility companies in balancing between the returns (from maximizing power production) and securing long term supply contracts at capped production. The production limitation set in the PPA has driven efforts to maximize profits through efficient and economic power production. In this paper, a combined industrial-scale gas turbine (GT) - absorption chiller (AC) system is considered to cool the GT air intake for reducing the plant’s heat rate (HR). This GT-AC system is optimized while considering power output limitations imposed by the PPA. In addition, the proposed formulation accounts for uncertainties in the ambient temperature using Type-2 fuzzy programming. Using the enhanced chaotic differential evolution (CEDE), the Pareto frontier was constructed and the optimization results are analyzed in detail.

Keywords: absorption chillers (AC), turbine inlet air cooling (TIC), power purchase agreement (PPA), multiobjective optimization, type-2 fuzzy programming, chaotic differential evolution (CDDE)

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Authors: Ali Albadri

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The logistics equation has never been used or studied in scientific fields outside the field of ecology. It has never been used to understand the behavior of a dynamic system of mechanical machines, like an escalator. We have studied the compatibility of the logistic map against real measurements from an escalator. This study has proven that there is good compatibility between the logistics equation and the experimental measurements. It has discovered the potential of a relationship between the fractal dimension and the non-linearity parameter, R, in the logistics equation. The fractal dimension increases as the R parameter (non-linear parameter) increases. It implies that the fractal dimension increases as the phase of the life span of the machine move from the steady/stable phase to the periodic double phase to a chaotic phase. The fractal dimension and the parameter R can be used as a tool to verify and check the health of machines. We have come up with a theory that there are three areas of behaviors, which they can be classified during the life span of a machine, a steady/stable stage, a periodic double stage, and a chaotic stage. The level of attention to the machine differs depending on the stage that the machine is in. The rate of faults in a machine increases as the machine moves through these three stages. During the double period and the chaotic stages, the number of faults starts to increase and become less predictable. The rate of predictability improves as our monitoring of the changes in the fractal dimension and the parameter R improves. The principles and foundations of our theory in this work have and will have a profound impact on the design of systems, on the way of operation of systems, and on the maintenance schedules of the systems. The systems can be mechanical, electrical, or electronic. The discussed methodology in this paper will give businesses the chance to be more careful at the design stage and planning for maintenance to control costs. The findings in this paper can be implied and used to correlate the three stages of a mechanical system to more in-depth mechanical parameters like wear and fatigue life.

Keywords: logistcs map, bifurcation map, fractal dimension, logistics equation

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Authors: Olga I. Moskalenko, Vladislav A. Khanadeev, Anastasya D. Koloskova, Alexey A. Koronovskii, Anatoly A. Pivovarov

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Generalized synchronization is one of the most intricate phenomena in nonlinear science. It can be observed both in systems with a unidirectional and mutual type of coupling including the complex networks. Such a phenomenon has a number of practical applications, for example, for the secure information transmission through the communication channel with a high level of noise. Known methods for the secure information transmission needs in the increase of the privacy of data transmission that arises a question about the observation of such phenomenon in systems with a complex topology of chaotic attractor possessing two or more positive Lyapunov exponents. The present report is devoted to the study of such phenomenon in two unidirectionally and mutually coupled dynamical systems being in chaotic (with one positive Lyapunov exponent) and hyperchaotic (with two or more positive Lyapunov exponents) regimes, respectively. As the systems under study, we have used two mutually coupled modified Lorenz oscillators and two unidirectionally coupled time-delayed generators. We have shown that in both cases the generalized synchronization regime can be detected by means of the calculation of Lyapunov exponents and phase tube approach whereas due to the complex topology of attractor the nearest neighbor method is misleading. Moreover, the auxiliary system approaches being the standard method for the synchronous regime observation, for the mutual type of coupling results in incorrect results. To calculate the Lyapunov exponents in time-delayed systems we have proposed an approach based on the modification of Gram-Schmidt orthogonalization procedure in the context of the time-delayed system. We have studied in detail the mechanisms resulting in the generalized synchronization regime onset paying a great attention to the field where one positive Lyapunov exponent has already been become negative whereas the second one is a positive yet. We have found the intermittency here and studied its characteristics. To detect the laminar phase lengths the method based on a calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been verified using the example of two unidirectionally coupled Rössler systems being in the band chaos regime. We have revealed the main characteristics of intermittency, i.e. the distribution of the laminar phase lengths and dependence of the mean length of the laminar phases on the criticality parameter, for all systems studied in the report. This work has been supported by the Russian President's Council grant for the state support of young Russian scientists (project MK-531.2018.2).

Keywords: complex topology of attractor, generalized synchronization, hyperchaos, Lyapunov exponents

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Authors: Mohammad Jalali Varnamkhasti

Abstract:

The genetic algorithms have been very successful in handling difficult optimization problems. The fundamental problem in genetic algorithms is premature convergence. This paper, present a new fuzzy genetic algorithm based on chaotic values instead of the random values in genetic algorithm processes. In this algorithm, for initial population is used chaotic sequences and then a new sexual selection proposed for selection mechanism. In this technique, the population is divided such that the male and female would be selected in an alternate way. The layout of the male and female chromosomes in each generation is different. A female chromosome is selected by tournament selection size from the female group. Then, the male chromosome is selected, in order of preference based on the maximum Hamming distance between the male chromosome and the female chromosome or The highest fitness value of male chromosome (if more than one male chromosome is having the maximum Hamming distance existed), or Random selection. The selections of crossover and mutation operators are achieved by running the fuzzy logic controllers, the crossover and mutation probabilities are varied on the basis of the phenotype and genotype characteristics of the chromosome population. Computational experiments are conducted on the proposed techniques and the results are compared with some other operators, heuristic and local search algorithms commonly used for solving p-median problems published in the literature.

Keywords: genetic algorithm, fuzzy system, chaos, sexual selection

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Authors: Abdon O. Makore

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The study analyses policy and institutional implications with regard to the successful implementation of IPTS in Harare. IPTS has widely been recommended as a rich solution to chaotic public transport operations, yet studies to determine the suitability or applicability of this concept have not been done in light of the existing transport institutions and policy framework in Harare. A predominantly qualitative research approach was employed backed by a deep scrutiny of the NTP and other subsidiary legislations and plans in place so as to ascertain the views and perceptions of various stakeholders regarding the proposed concept. As such, key informant interviews, unstructured interviews, and questionnaires were vital tools in gathering data and these were effectively buttressed by observations, photography, and documentary analysis. The study revealed from a policy perspective that there are high prospects for the implementation of IPTS in Harare as the existing NTP, subsidiary legislations and plans do have provisions for the concept backed by keen interest of all responsible urban public transport authorities. However, there is lack of coherent and systematic approach among other responsible institutions, as such recommendations formulated advocated for institutional integration and strong political will for the ultimate success of the concept.

Keywords: integrated public transport system, policy, legislation, institutions

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Authors: Mitsuyoshi Tomiya, Kentaro Kawamura, Shoichi Sakamoto

Abstract:

In chaotic billiard systems, scar-like localization has been found on time-evolving wave packet. We may call it the “dynamical scar” to separate it to the original scar in stationary states. It also comes out along the vicinity of classical unstable periodic orbits, when the wave packets are launched along the orbits, against the hypothesis that the waves become homogenous all around the billiard. Then time-evolving wave packets are investigated numerically in phase space. The Wigner function is adopted to detect the wave packets in phase space. The 2-dimensional Poincaré sections of the 4-dimensional phase space are introduced to clarify the dynamical behavior of the wave packets. The Poincaré sections of the coordinate (x or y) and the momentum (Px or Py) can visualize the dynamical behavior of the wave packets, including the behavior in the momentum degree also. For example, in “dynamical scar” states, a bit larger momentum component comes first, and then the a bit smaller and smaller components follow next. The sections made in the momentum space (Px or Py) elucidates specific trajectories that have larger contribution to the “dynamical scar” states. It is the fixed point observation of the momentum degrees at a specific fixed point(x0, y0) in the phase space. The accumulation are also calculated to search the “dynamical scar” in the Poincare sections. It is found the scars as bright spots in momentum degrees of the phase space.

Keywords: chaotic billiard, Poincaré section, scar, wave packet

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