Search results for: chaotic systems.
4434 Synchronization Between Two Chaotic Systems: Numerical and Circuit Simulation
Authors: J. H. Park, T. H. Lee, S. M. Lee, H. Y. Jung
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In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
Keywords: Chaotic systems, synchronization, Lyapunov method, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16714433 Fundamental Groups in Chaotic Flat Space and Its Retractions
Authors: A. E. El-Ahmady, M. Abu-Saleem
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The purpose of this paper is to give a combinatorial characterization and construct representations of the chaotic fundamental groups of the chaotic submanifolds of chaotic flat space by using some geometrical transformations. The chaotic homotopy groups of the limit folding for chaotic flat space are presented. The chaotic fundamental groups of some types of chaotic geodesics in chaotic flat space are deduced.
Keywords: Chaotic flat space, Chaotic folding, Chaotic retractions, Chaotic fundamental groups.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15214432 Synchronization of Non-Identical Chaotic Systems with Different Orders Based On Vector Norms Approach
Authors: Rihab Gam, Anis Sakly, Faouzi M'sahli
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17894431 H∞ Approach to Functional Projective Synchronization for Chaotic Systems with Disturbances
Authors: S. M. Lee, J. H. Park, H. Y. Jung
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This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constraint.
Keywords: Chaotic systems, functional projective H∞ synchronization, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12954430 Design of a Chaotic Trajectory Generator Algorithm for Mobile Robots
Authors: J. J. Cetina-Denis, R. M. López-Gutiérrez, R. Ramírez-Ramírez, C. Cruz-Hernández
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7074429 Finite Time Symplectic Synchronization between Two Different Chaotic Systems
Authors: Chunming Xu
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In this paper, the finite-time symplectic synchronization between two different chaotic systems is investigated. Based on the finite-time stability theory, a simple adaptive feedback scheme is proposed to realize finite-time symplectic synchronization for the Lorenz and L¨u systems. Numerical examples are provided to show the effectiveness of the proposed method.Keywords: Chaotic systems, symplectic synchronization, finite-time synchronization, adaptive controller.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9494428 Chaotic Behavior in Monetary Systems: Comparison among Different Types of Taylor Rule
Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17424427 New Class of Chaotic Mappings in Symbol Space
Authors: Inese Bula
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Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.
Keywords: Infinite symbol space, prefix metric, chaotic mapping, generator function, jump mapping.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15064426 A Two-Channel Secure Communication Using Fractional Chaotic Systems
Authors: Long Jye Sheu, Wei Ching Chen, Yen Chu Chen, Wei Tai Weng
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17354425 Encrypted Audio Communication Based On Synchronized Unified Chaotic Systems
Authors: C. Cruz-Hernández, E. Inzunza-González, R.M. López-Gutiérrez H. Serrano-Guerrero, E.E.García-Guerrero
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16884424 Bidirectional Chaotic Synchronization of Non-Autonomous Circuit and its Application for Secure Communication
Authors: Mada Sanjaya, Halimatussadiyah, Dian Syah Maulana
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The nonlinear chaotic non-autonomous fourth order system is algebraically simple but can generate complex chaotic attractors. In this paper, non-autonomous fourth order chaotic oscillator circuits were designed and simulated. Also chaotic nonautonomous Attractor is addressed suitable for chaotic masking communication circuits using Matlab® and MultiSIM® programs. We have demonstrated in simulations that chaos can be synchronized and applied to signal masking communications. We suggest that this phenomenon of chaos synchronism may serve as the basis for little known chaotic non-autonomous Attractor to achieve signal masking communication applications. Simulation results are used to visualize and illustrate the effectiveness of non-autonomous chaotic system in signal masking. All simulations results performed on nonautonomous chaotic system are verify the applicable of secure communication.Keywords: Bidirectional chaotic synchronization, double bellattractor, secure communication
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21654423 Control of Chaotic Dynamical Systems using RBF Networks
Authors: Yoichi Ishikawa, Yuichi Masukake, Yoshihisa Ishida
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16314422 Global Chaos Synchronization of Identical and Nonidentical Chaotic Systems Using Only Two Nonlinear Controllers
Authors: Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad, Israr Ahmad
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In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.
Keywords: Nonlinear Active Control, Chen and Tigan Chaotic systems, Lyapunov Stability theory, Synchronization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19484421 Performance of Chaotic Lu System in CDMA Satellites Communications Systems
Authors: K. Kemih, M. Benslama
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This paper investigates the problem of spreading sequence and receiver code synchronization techniques for satellite based CDMA communications systems. The performance of CDMA system depends on the autocorrelation and cross-correlation properties of the used spreading sequences. In this paper we propose the uses of chaotic Lu system to generate binary sequences for spreading codes in a direct sequence spread CDMA system. To minimize multiple access interference (MAI) we propose the use of genetic algorithm for optimum selection of chaotic spreading sequences. To solve the problem of transmitter-receiver synchronization, we use the passivity controls. The concept of semipassivity is defined to find simple conditions which ensure boundedness of the solutions of coupled Lu systems. Numerical results are presented to show the effectiveness of the proposed approach.Keywords: About Chaotic Lu system, synchronization, Spreading sequence, Genetic Algorithm. Passive System
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17314420 Backstepping Design and Fractional Derivative Equation of Chaotic System
Authors: Ayub Khan, Net Ram Garg, Geeta Jain
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In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.
Keywords: Backstepping method, Fractional order, Synchronization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21314419 Study on the Chaotic Cipher Combined with Mersenne Twister
Authors: Daiki Yoshida, Ariyoshi Nakayama, Hirotaka Watanabe, Taichi Sato, Syuhei Kuriyama, Hiroyuki Kamata
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18844418 Stabilization of the Lorenz Chaotic Equations by Fuzzy Controller
Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi
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In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.Keywords: Chaotic system, Fuzzy control, Lorenz equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20144417 Anti-Synchronization of two Different Chaotic Systems via Active Control
Authors: Amir Abbas Emadzadeh, Mohammad Haeri
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This paper presents anti-synchronization of chaos between two different chaotic systems using active control method. The proposed technique is applied to achieve chaos antisynchronization for the Lü and Rössler dynamical systems. Numerical simulations are implemented to verify the results.Keywords: Active control, Anti-Synchronization, Chaos, Lü system, Rössler system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19064416 Synthesis of a Control System of a Deterministic Chaotic Process in the Class of Two-Parameter Structurally Stable Mappings
Authors: M. Beisenbi, A. Sagymbay, S. Beisembina, A. Satpayeva
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In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.
Keywords: Control system synthesis, deterministic chaotic processes, Lyapunov vector function, robust stability, structurally stable mappings.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3634415 Pseudo-almost Periodic Solutions of a Class Delayed Chaotic Neural Networks
Authors: Farouk Cherif
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This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.
Keywords: Chaotic neural network, Hamiltonian systems, Pseudo almost periodic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12994414 GPI Observer-based Tracking Control and Synchronization of Chaotic Systems
Authors: Dangjun Zhao, Yongji Wang, Lei Liu
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Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.
Keywords: GPI observer, sliding mode control, master-slave synchronization, chaotic systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19854413 Unscented Transformation for Estimating the Lyapunov Exponents of Chaotic Time Series Corrupted by Random Noise
Authors: K. Kamalanand, P. Mannar Jawahar
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Many systems in the natural world exhibit chaos or non-linear behavior, the complexity of which is so great that they appear to be random. Identification of chaos in experimental data is essential for characterizing the system and for analyzing the predictability of the data under analysis. The Lyapunov exponents provide a quantitative measure of the sensitivity to initial conditions and are the most useful dynamical diagnostic for chaotic systems. However, it is difficult to accurately estimate the Lyapunov exponents of chaotic signals which are corrupted by a random noise. In this work, a method for estimation of Lyapunov exponents from noisy time series using unscented transformation is proposed. The proposed methodology was validated using time series obtained from known chaotic maps. In this paper, the objective of the work, the proposed methodology and validation results are discussed in detail.
Keywords: Lyapunov exponents, unscented transformation, chaos theory, neural networks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19754412 A Double Differential Chaos Shift Keying Scheme for Ultra-Wideband Chaotic Communication Technology Applied in Low-Rate Wireless Personal Area Network
Authors: Ghobad Gorji, Hasan Golabi
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1844411 Dense Chaos in Coupled Map Lattices
Authors: Tianxiu Lu, Peiyong Zhu
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This paper is mainly concerned with a kind of coupled map lattices (CMLs). New definitions of dense δ-chaos and dense chaos (which is a special case of dense δ-chaos with δ = 0) in discrete spatiotemporal systems are given and sufficient conditions for these systems to be densely chaotic or densely δ-chaotic are derived.
Keywords: Discrete spatiotemporal systems, coupled map lattices, dense δ-chaos, Li-Yorke pairs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16464410 Encrypter Information Software Using Chaotic Generators
Authors: Cardoza-Avendaño L., López-Gutiérrez R.M., Inzunza-González E., Cruz-Hernández C., García-Guerrero E., Spirin V., Serrano H.
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This document shows a software that shows different chaotic generator, as continuous as discrete time. The software gives the option for obtain the different signals, using different parameters and initial condition value. The program shows then critical parameter for each model. All theses models are capable of encrypter information, this software show it too.
Keywords: cryptography, chaotic attractors, software.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14804409 A Very Efficient Pseudo-Random Number Generator Based On Chaotic Maps and S-Box Tables
Authors: M. Hamdi, R. Rhouma, S. Belghith
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Generating random numbers are mainly used to create secret keys or random sequences. It can be carried out by various techniques. In this paper we present a very simple and efficient pseudo random number generator (PRNG) based on chaotic maps and S-Box tables. This technique adopted two main operations one to generate chaotic values using two logistic maps and the second to transform them into binary words using random S-Box tables. The simulation analysis indicates that our PRNG possessing excellent statistical and cryptographic properties.
Keywords: Chaotic map, Cryptography, Random Numbers, Statistical tests, S-box.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 38544408 Hopf Bifurcation for a New Chaotic System
Authors: Kejun Zhuang
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In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.
Keywords: Chaotic system, Hopf bifurcation, normal form theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14394407 Synchronization of Chaos in a Food Web in Ecological Systems
Authors: Anuraj Singh, Sunita Gakkhar
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The three-species food web model proposed and investigated by Gakkhar and Naji is known to have chaotic behaviour for a choice of parameters. An attempt has been made to synchronize the chaos in the model using bidirectional coupling. Numerical simulations are presented to demonstrate the effectiveness and feasibility of the analytical results. Numerical results show that for higher value of coupling strength, chaotic synchronization is achieved. Chaos can be controlled to achieve stable synchronization in natural systems.
Keywords: Lyapunov Exponent, Bidirectional Coupling, ChaosSynchronization, Synchronization Manifold
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13004406 Avoiding Catastrophic Forgetting by a Dual-Network Memory Model Using a Chaotic Neural Network
Authors: Motonobu Hattori
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In neural networks, when new patterns are learned by a network, the new information radically interferes with previously stored patterns. This drawback is called catastrophic forgetting or catastrophic interference. In this paper, we propose a biologically inspired neural network model which overcomes this problem. The proposed model consists of two distinct networks: one is a Hopfield type of chaotic associative memory and the other is a multilayer neural network. We consider that these networks correspond to the hippocampus and the neocortex of the brain, respectively. Information given is firstly stored in the hippocampal network with fast learning algorithm. Then the stored information is recalled by chaotic behavior of each neuron in the hippocampal network. Finally, it is consolidated in the neocortical network by using pseudopatterns. Computer simulation results show that the proposed model has much better ability to avoid catastrophic forgetting in comparison with conventional models.
Keywords: catastrophic forgetting, chaotic neural network, complementary learning systems, dual-network
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20844405 Dynamics and Control of a Chaotic Electromagnetic System
Authors: Shun-Chang Chang
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In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.
Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1589