Search results for: Chaos.

Authors: Jixiang Zhang, Guocheng Wang

Abstract:

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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Authors: Madiha Tariq, Hena Rabbani

Abstract:

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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Authors: Ghobad Gorji, Hasan Golabi

Abstract:

The goal of this paper is to describe the design of an ultra-wideband (UWB) system that is optimized for the low-rate wireless personal area network application. To this aim, we propose a system based on direct chaotic communication (DCC) technology. Based on this system, a 2-GHz wide chaotic signal is produced into the UWB spectrum lower band, i.e., 3.1–5.1 GHz. For this system, two simple modulation schemes, namely chaotic on-off keying (COOK) and differential chaos shift keying  (DCSK) are evaluated first. We propose a modulation scheme, namely Double DCSK, to improve the performance of UWB DCC. Different characteristics of these systems, with Monte Carlo simulations based on the Additive White Gaussian Noise (AWGN) and the IEEE 802.15.4a standard channel models, are compared.

Keywords: Ultra-wideband, UWB, Direct Chaotic Communication, DCC, IEEE 802.15.4a, COOK, DCSK.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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Authors: Randhir Singh Baghel, Joydip Dhar, Renu Jain

Abstract:

In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain. Here, the susceptible phytoplankton is growing logistically and the growth of infected phytoplankton is due to the instantaneous Holling type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain. It is also observe that the reaction diffusion system exhibits spatiotemporal chaos and pattern formation in phytoplankton dynamics, which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern formation.

Keywords: Phytoplankton dynamics, Reaction-diffusion system, Local stability, Hopf-bifurcation, Global stability, Chaos, Pattern Formation, Higher-order stability analysis.

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Authors: Helle Hein, Ülo Lepik

Abstract:

A gradient learning method to regulate the trajectories of some nonlinear chaotic systems is proposed. The method is motivated by the gradient descent learning algorithms for neural networks. It is based on two systems: dynamic optimization system and system for finding sensitivities. Numerical results of several examples are presented, which convincingly illustrate the efficiency of the method.

Keywords: Chaos, Dynamical Systems, Learning, Neural Networks

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Authors: S. Behnia, S. Fathizadeh

Abstract:

Conductivity properties of DNA molecule is investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model. This model is a tight-binding linear nanoscale chain. We have tried to study the electrical current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram.

Keywords: Charge transfer in DNA, Chaos theory, Molecular electronics, Negative Differential resistance.

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Authors: C. Cruz-Hernández, E. Inzunza-González, R.M. López-Gutiérrez H. Serrano-Guerrero, E.E.García-Guerrero

Abstract:

In this paper, encrypted audio communications based on synchronization of coupled unified chaotic systems in master-slave configuration is numerically studied. We transmit the encrypted audio messages by using two unsecure channels. Encoding, transmission, and decoding audio messages in chaotic communication is presented.

Keywords: Audio encrypted, chaos, synchronization.

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Authors: S. Ben Said, K. Ben Saad, M. Benrejeb

Abstract:

This paper deals with bifurcation analyses in current programmed DC/DC Boost converter and exhibition of chaotic behavior. This phenomenon occurs due to variation of a set of the studied circuit parameters (input voltage and a reference current). Two different types of bifurcation paths have been observed as part as part of another bifurcation arising from variation of suitable chosen parameter.

Keywords: Bifurcation, Chaos, Boost converter, Current- programmed control, Initial parameters.

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Authors: Yoichi Ishikawa, Yuichi Masukake, Yoshihisa Ishida

Abstract:

This paper presents a novel control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. The proposed method first identifies the nonlinear part of the chaotic system off-line and then constructs a model-following controller using only the estimated system parameters. Simulation results show the effectiveness of the proposed control scheme.

Keywords: Chaos, nonlinear plant, radial basis function network.

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Authors: Long Jye Sheu, Wei Ching Chen, Yen Chu Chen, Wei Tai Weng

Abstract:

In this paper, a two-channel secure communication using fractional chaotic systems is presented. Conditions for chaos synchronization have been investigated theoretically by using Laplace transform. To illustrate the effectiveness of the proposed scheme, a numerical example is presented. The keys, key space, key selection rules and sensitivity to keys are discussed in detail. Results show that the original plaintexts have been well masked in the ciphertexts yet recovered faithfully and efficiently by the present schemes.

Keywords: fractional chaotic systems, synchronization, securecommunication.

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Authors: Anton V. Doroshin

Abstract:

This article contains a description of main ideas for the attitude reorientation of spacecraft (small dual-spin spacecraft, nanosatellites) using properties of its chaotic attitude motion under the action of internal perturbations. The considering method based on intentional initiations of chaotic modes of the attitude motion with big amplitudes of the nutation oscillations, and also on the redistributions of the angular momentum between coaxial bodies of the dual-spin spacecraft (DSSC), which perform in the purpose of system’s phase space changing.

Keywords: Spacecraft, Attitude Dynamics and Control, Chaos.

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Authors: Majid Reza Naseh, Mohammad Haeri

Abstract:

This paper introduces an adaptive control scheme to synchronize two identical Chua's systems. Introductory part of the paper is presented in the first part of the paper and then in the second part, a new theorem is proposed based on which an adaptive control scheme is developed to synchronize two identical modified Chua's circuit. Finally, numerical simulations are included to verify the effectiveness of the proposed control method.

Keywords: Chaos synchronization, adaptive control, Chua's circuits.

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Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao

Abstract:

The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: Chaos theory, GMM estimator, Lyapunov Exponent, Monetary System, Taylor Rule.

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Authors: Daiki Yoshida, Ariyoshi Nakayama, Hirotaka Watanabe, Taichi Sato, Syuhei Kuriyama, Hiroyuki Kamata

Abstract:

In this study, we propose the chaotic cipher combined with Mersenne Twister that is an extremely good pseudo-random number generator for the secure communications. We investigate the Lyapunov exponent of the proposed system, and evaluate the randomness performance by comparing RC4 and the chaotic cipher. In these results, our proposed system gets high chaotic property and more randomness than the conventional ciphers.

Keywords: Chaos, chaotic property, cipher, Mersenne Twister, Randomness.

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Authors: R.M. López-Gutiérrez, C. Cruz-Hernández, C. Posadas-Castillo, E.E.García-Guerrero

Abstract:

Encoded information based on synchronization of coupled chaotic Nd:YAG lasers in master-slave configuration is numerically studied. Encoding, transmission, and decoding of information in optical chaotic communication with a single channel is presented. We analyze the robustness of the encrypted audio transmission in a channel noise. In order to illustrate this synchronization robustness, we present two cases of study: synchronization and transmission with a single channel without and with noise in the channel.

Keywords: Encryption, Secure coomunication, Chaos, Synchronization, Complex networks, Nd:YAG laser.

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Authors: Rihab Gam, Anis Sakly, Faouzi M'sahli

Abstract:

A new strategy of control is formulated for chaos synchronization of non-identical chaotic systems with different orders using the Borne and Gentina practical criterion associated with the Benrejeb canonical arrow form matrix, to drift the stability property of dynamic complex systems. The designed controller ensures that the state variables of controlled chaotic slave systems globally synchronize with the state variables of the master systems, respectively. Numerical simulations are performed to illustrate the efficiency of the proposed method.

Keywords: Synchronization, Non-identical chaotic systems, Different orders, Arrow form matrix.

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Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi

Abstract:

In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.

Keywords: Memristor, chaotic circuit, dynamical behavior, chaotic system.

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Authors: J. J. Cetina-Denis, R. M. López-Gutiérrez, R. Ramírez-Ramírez, C. Cruz-Hernández

Abstract:

This work addresses the problem of designing an algorithm capable of generating chaotic trajectories for mobile robots. Particularly, the chaotic behavior is induced in the linear and angular velocities of a Khepera III differential mobile robot by infusing them with the states of the H´enon chaotic map. A possible application, using the properties of chaotic systems, is patrolling a work area. In this work, numerical and experimental results are reported and analyzed. In addition, two quantitative numerical tests are applied in order to measure how chaotic the generated trajectories really are.

Keywords: Chaos, chaotic trajectories, differential mobile robot, Henons map, Khepera III robot, patrolling applications.

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Authors: Hongmin Deng, Qionghua Wang

Abstract:

A modified two dimensional (2D) logistic map based on cross feedback control is proposed. This 2D map exhibits more random chaotic dynamical properties than the classic one dimensional (1D) logistic map in the statistical characteristics analysis. So it is utilized as the pseudo-random (PN) sequence generator, where the obtained real-valued PN sequence is quantized at first, then applied to radio frequency identification (RFID) communication system in this paper. This system is experimentally validated on a cortex-M₀ development board, which shows the effectiveness in key generation, the size of key space and security. At last, further cryptanalysis is studied through the test suite in the National Institute of Standards and Technology (NIST).

Keywords: Chaos encryption, logistic map, pseudo-random sequence, RFID.

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Authors: Ramesh K. Sunkaria

Abstract:

The linear methods of heart rate variability analysis such as non-parametric (e.g. fast Fourier transform analysis) and parametric methods (e.g. autoregressive modeling) has become an established non-invasive tool for marking the cardiac health, but their sensitivity and specificity were found to be lower than expected with positive predictive value <30%. This may be due to considering the RR-interval series as stationary and re-sampling them prior to their use for analysis, whereas actually it is not. This paper reviews the non-linear methods of HRV analysis such as correlation dimension, largest Lyupnov exponent, power law slope, fractal analysis, detrended fluctuation analysis, complexity measure etc. which are currently becoming popular as these uses the actual RR-interval series. These methods are expected to highly accurate cardiac health prognosis.

Keywords: chaos, nonlinear dynamics, sample entropy, approximate entropy, detrended fluctuation analysis.

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Authors: Mohammad H. Fattahi

Abstract:

Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. Noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: Chaotic behavior, wavelet, noise reduction, river flow.

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Authors: Thang Manh Hoang

Abstract:

Recent research result has shown that two multidelay feedback systems can synchronize each other under different schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating synchronization. There, the driving signal is significantly complex due that it is constituted by multiple nonlinear transformations of delayed state variable. In this paper, a secure communication model is proposed based on synchronization of coupled multidelay feedback systems, in which the plain signal is mixed with a complex signal at the transmitter side and it is precisely retrieved at the receiver side. The effectiveness of the proposed model is demonstrated and verified in the specific example, where the message signal is masked directly by the complex signal and security is examined under the breaking method of power spectrum analysis.

Keywords: chaos synchronization, time-delayed system, chaosbasedsecure communications

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Authors: M. Lloret-Climent, J. Nescolarde-Selva

Abstract:

The aim of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on a pre-designed algorithm and applying our interpretation of chaos theory developed in the context of General Systems Theory. This article sets out the causal relationships associated with tourist flows in order to enable the formulation of appropriate strategies. Our results can be applied to numerous cases. For example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups and to analyse tourist behaviour in terms of the most relevant variables. Unlike statistical analyses that merely provide information on current data, our method uses orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.

Keywords: Attractor, invariant set, orbits, tourist variables.

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Authors: Hirotaka Watanabe, Takaaki Kondo, Daiki Yoshida, Ariyoshi Nakayama, Taichi Sato, Shuhei Kuriyama, Hiroyuki Kamata

Abstract:

In this paper, we propose a chaotic cipher system consisting of Improved Volterra Filters and the mapping that is created from the actual voice by using Radial Basis Function Network. In order to achieve a practical system, the system supposes to use the digital communication line, such as the Internet, to maintain the parameter matching between the transmitter and receiver sides. Therefore, in order to withstand the attack from outside, it is necessary that complicate the internal state and improve the sensitivity coefficient. In this paper, we validate the robustness of proposed method from three perspectives of "Chaotic properties", "Randomness", "Coefficient sensitivity".

Keywords: Chaos cipher, 16-bit-length fixed point arithmetic, Volterra filter, Seacret communications, RBF Network

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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Authors: Yizhi Gai, Yukinori Kobayashi, Yohei Hoshino, Takanori Emaru

Abstract:

Motion control of flexible arms is more difficult than that of rigid arms, however utilizing its dynamics enables improved performance such as a fast motion in short operation time. This paper investigates a ball throwing robot with one rigid link and one flexible link. This robot throws a ball at a set speed with a proper control torque. A mathematical model of this ball throwing robot is derived through Hamilton’s principle. Several patterns of torque input are designed and tested through the proposed simulation models. The parameters of each torque input pattern is optimized and determined by chaos embedded vector evaluated particle swarm optimization (CEVEPSO). Then, the residual vibration of the manipulator after throwing is suppressed with input shaping technique. Finally, a real experiment is set up for the model checking.

Keywords: Motion control, flexible robotic arm, CEVEPSO, ball throwing robot.

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Authors: Cai-Wan Chang-Jian

Abstract:

This study presents a systematic analysis of the dynamic behaviors of a gear-bearing system with porous squeeze film damper (PSFD) under nonlinear suspension, nonlinear oil-film force and nonlinear gear meshing force effect. It can be found that the system exhibits very rich forms of sub-harmonic and even the chaotic vibrations. The bifurcation diagrams also reveal that greater values of permeability may not only improve non-periodic motions effectively, but also suppress dynamic amplitudes of the system. Therefore, porous effect plays an important role to improve dynamic stability of gear-bearing systems or other mechanical systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

Keywords: Gear, PSFD, bifurcation, chaos.

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Authors: S. Mahmoodzadeh, J. Shahrabi, M. A. Torkamani, J. Sabaghzadeh Ghomi

Abstract:

Recognizing behavioral patterns of financial markets is essential for traders. Japanese candlestick chart is a common tool to visualize and analyze such patterns in an economic time series. Since the world was introduced to Japanese candlestick charting, traders saw how combining this tool with intelligent technical approaches creates a powerful formula for the savvy investors. This paper propose a generalization to box counting method of Grassberger-Procaccia, which is based on computing the correlation dimension of Japanese candlesticks instead commonly used 'close' points. The results of this method applied on several foreign exchange rates vs. IRR (Iranian Rial). Satisfactorily show lower chaotic dimension of Japanese candlesticks series than regular Grassberger-Procaccia method applied merely on close points of these same candles. This means there is some valuable information inside candlesticks.

Keywords: Chaos, Japanese candlestick, generalized box counting, strange attractor.

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Authors: Kelvin Rozier, Vladimir E. Bondarenko

Abstract:

It is known that an analog Hopfield neural network with time delay can generate the outputs which are similar to the human electroencephalogram. To gain deeper insights into the mechanisms of rhythm generation by the Hopfield neural networks and to study the effects of noise on their activities, we investigated the behaviors of the networks with symmetric and asymmetric interneuron connections. The neural network under the study consists of 10 identical neurons. For symmetric (fully connected) networks all interneuron connections aij = +1; the interneuron connections for asymmetric networks form an upper triangular matrix with non-zero entries aij = +1. The behavior of the network is described by 10 differential equations, which are solved numerically. The results of simulations demonstrate some remarkable properties of a Hopfield neural network, such as linear growth of outputs, dependence of synchronization properties on the connection type, huge amplification of oscillation by the external uniform noise, and the capability of the neural network to transform one type of noise to another.

Keywords: Chaos, Hopfield neural network, noise, synchronization

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