Synchronization of two different chaotic systems via nonlinear ...

African Journals Online (AJOL)

ADOWIE PERE

ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.

Robust synchronization of chaotic systems via feedback

Energy Technology Data Exchange (ETDEWEB)

Femat, Ricardo [IPICYT, San Luis Potosi (Mexico). Dept. de Matematicas Aplicadas; Solis-Perales, Gualberto [Universidad de Guadalajara, Centro Univ. de Ciencias Exactas e Ingenierias (Mexico). Div. de Electronica y Computacion

2008-07-01

This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems. (orig.)

Qualitative feature extractions of chaotic systems

International Nuclear Information System (INIS)

Vicha, T.; Dohnal, M.

2008-01-01

The theory of chaos offers useful tools for systems analysis. However, models of complex systems are based on a network of inconsistent, space and uncertain knowledge items. Traditional quantitative methods of chaos analysis are therefore not applicable. The paper by the same authors [Vicha T, Dohnal M. Qualitative identification of chaotic systems behaviours. Chaos, Solitons and Fractals, in press, [Log. No. 601019] ] presents qualitative interpretation of some chaos concepts. There are only three qualitative values positive/increasing, negative/decreasing and zero/constant. It means that any set of qualitative multidimensional descriptions of unsteady state behaviours is discrete and finite. A finite upper limit exists for the total number of qualitatively distinguishable scenarios. A set of 21 published chaotic models is solved qualitatively and 21 sets of all existing qualitative scenarios are presented. The intersection of all 21 scenario sets is empty. There is no such a behaviour which is common for all 21 models. The set of 21 qualitative models (e.g. Lorenz, Roessler) can be used to compare chaotic behaviours of an unknown qualitative model with them to evaluate if its chaotic behaviours is close to e.g. Lorenz chaotic model and how much

A novel image block cryptosystem based on a spatiotemporal chaotic system and a chaotic neural network

International Nuclear Information System (INIS)

Wang Xing-Yuan; Bao Xue-Mei

2013-01-01

In this paper, we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN). The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL), where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters. The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML), which can be easily implemented in parallel by hardware. A 160-bit-long binary sequence is used to generate the initial conditions of the CML. The decryption process is symmetric relative to the encryption process. Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical, and suitable for image encryption. (general)

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

International Nuclear Information System (INIS)

Hong-Yan, Jia; Zeng-Qiang, Chen; Zhu-Zhi, Yuan

2010-01-01

By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation. (general)

Parametric Control on Fractional-Order Response for Lü Chaotic System

KAUST Repository

Moaddy, K; Radwan, A G; Salama, Khaled N.; Momani, S; Hashim, I

2013-01-01

This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.

Parametric Control on Fractional-Order Response for Lü Chaotic System

KAUST Repository

Moaddy, K

2013-04-10

This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.

Adaptive Synchronization of Memristor-based Chaotic Neural Systems

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Xiaofang Hu

2014-11-01

Full Text Available Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

A novel 3D autonomous system with different multilayer chaotic attractors

International Nuclear Information System (INIS)

Dong Gaogao; Du Ruijin; Tian Lixin; Jia Qiang

2009-01-01

This Letter proposes a novel three-dimensional autonomous system which has complex chaotic dynamics behaviors and gives analysis of novel system. More importantly, the novel system can generate three-layer chaotic attractor, four-layer chaotic attractor, five-layer chaotic attractor, multilayer chaotic attractor by choosing different parameters and initial condition. We analyze the new system by means of phase portraits, Lyapunov exponent spectrum, fractional dimension, bifurcation diagram and Poincare maps of the system. The three-dimensional autonomous system is totally different from the well-known systems in previous work. The new multilayer chaotic attractors are also worth causing attention.

Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems

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Hossein Shokouhi-Nejad

2014-01-01

Full Text Available This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.

A non-correlator-based digital communication system using interleaved chaotic differential peaks keying (I-CDPK) modulation and chaotic synchronization

International Nuclear Information System (INIS)

Chien, T.-I; Hung, Y.-C.; Liao, T.-L.

2006-01-01

This paper presents a novel non-correlator-based digital communication system with the application of interleaved chaotic differential peaks keying (I-CDPK) modulation technique. The proposed communication system consists of four major modules: I-CDPK modulator (ICM), frequency modulation (FM) transmitter, FM receiver and I-CDPK demodulator (ICDM). In the ICM module, there are four components: a chaotic circuit to generate the chaotic signals, A/D converter, D/A converter and a digital processing mechanism to control all signal flows and performs I-CDPK modulation corresponding to the input digital bits. For interleaving every input digital bit set, every state of the chaotic system is used to represent one portion of it, but only a scalar state variable (i.e. the system output) is sent to the ICDM's chaotic circuit through both FM transmitter and FM receiver. An observer-based chaotic synchronization scheme is designed to synchronize the chaotic circuits of the ICM and ICDM. Meanwhile, the bit detector in ICDM is devoted to recover the transmitted input digital bits. Some numerical simulations of an illustrative communication system are given to demonstrate its theoretical effectiveness. Furthermore, the performance of bit error rate of the proposed system is analyzed and compared with those of the correlator-based communication systems adopting coherent binary phase shift keying (BPSK) and coherent differential chaotic shift keying (DCSK) schemes

Non-reversible evolution of quantum chaotic system. Kinetic description

International Nuclear Information System (INIS)

Chotorlishvili, L.; Skrinnikov, V.

2008-01-01

It is well known that the appearance of non-reversibility in classical chaotic systems is connected with a local instability of phase trajectories relatively to a small change of initial conditions and parameters of the system. Classical chaotic systems reveal an exponential sensitivity to these changes. This leads to an exponential growth of initial error with time, and as the result after the statistical averaging over this error, the dynamics of the system becomes non-reversible. In spite of this, the question about the origin of non-reversibility in quantum case remains actual. The point is that the classical notion of instability of phase trajectories loses its sense during quantum consideration. The current work is dedicated to the clarification of the origin of non-reversibility in quantum chaotic systems. For this purpose we study a non-stationary dynamics of the chaotic quantum system. By analogy with classical chaos, we consider an influence of a small unavoidable error of the parameter of the system on the non-reversibility of the dynamics. It is shown in the Letter that due to the peculiarity of chaotic quantum systems, the statistical averaging over the small unavoidable error leads to the non-reversible transition from the pure state into the mixed one. The second part of the Letter is dedicated to the kinematic description of the chaotic quantum-mechanical system. Using the formalism of superoperators, a muster kinematic equation for chaotic quantum system was obtained from Liouville equation under a strict mathematical consideration

Synchronizing a class of uncertain chaotic systems

International Nuclear Information System (INIS)

Chen Maoyin; Zhou Donghua; Shang Yun

2005-01-01

This Letter deals with the synchronization of a class of uncertain chaotic systems in the drive-response framework. A robust adaptive observer based response system is designed to synchronize a given chaotic system with unknown parameters and external disturbances. Lyapunov stability ensures the global synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of Genesio-Tesi system verifies the effectiveness of this scheme

Generalized projective synchronization of a unified chaotic system

International Nuclear Information System (INIS)

Yan Jianping; Li Changpin

2005-01-01

In the present paper, a simple but efficient control technique of the generalized projective synchronization is applied to a unified chaotic system. Numerical simulations show that this method works very well, which can also be applied to other chaotic systems

Chaos synchronization between two different chaotic dynamical systems

International Nuclear Information System (INIS)

Park, Ju H.

2006-01-01

This work presents chaos synchronization between two different chaotic systems by nonlinear control laws. First, synchronization problem between Genesio system and Rossler system has been investigated, and then the similar approach is applied to the synchronization problem between Genesio system and a new chaotic system developed recently in the literature. The control performances are verified by two numerical examples

Modelling chaotic Hamiltonian systems as a Markov Chain ...

African Journals Online (AJOL)

The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...

Modified scaling function projective synchronization of chaotic systems

International Nuclear Information System (INIS)

Xu Yu-Hua; Zhou Wu-Neng; Fang Jian-An

2011-01-01

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method. (general)

A New Chaotic System with Positive Topological Entropy

Directory of Open Access Journals (Sweden)

Zhonglin Wang

2015-08-01

Full Text Available This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are analyzed via Lyapunov exponent spectrum, bifurcation diagrams, phase portraits and the Poincaré map. The compound structures of this new system are also analyzed. By means of topological horseshoe theory and numerical computation, the Poincaré map defined for the system is proved to be semi-conjugate to 3-shift map, and thus the system has positive topological entropy.

An optical CDMA system based on chaotic sequences

Science.gov (United States)

Liu, Xiao-lei; En, De; Wang, Li-guo

2014-03-01

In this paper, a coherent asynchronous optical code division multiple access (OCDMA) system is proposed, whose encoder/decoder is an all-optical generator. This all-optical generator can generate analog and bipolar chaotic sequences satisfying the logistic maps. The formula of bit error rate (BER) is derived, and the relationship of BER and the number of simultaneous transmissions is analyzed. Due to the good property of correlation, this coherent OCDMA system based on these bipolar chaotic sequences can support a large number of simultaneous users, which shows that these chaotic sequences are suitable for asynchronous OCDMA system.

Implementation of chaotic secure communication systems based on OPA circuits

International Nuclear Information System (INIS)

Huang, C.-K.; Tsay, S.-C.; Wu, Y.-R.

2005-01-01

In this paper, we proposed a novel three-order autonomous circuit to construct a chaotic circuit with double scroll characteristic. The design idea is to use RLC elements and a nonlinear resistor. The one of salient features of the chaotic circuit is that the circuit with two flexible breakpoints of nonlinear element, and the advantage of the flexible breakpoint is that it increased complexity of the dynamical performance. Here, if we take a large and suitable breakpoint value, then the chaotic state can masking a large input signal in the circuit. Furthermore, we proposed a secure communication hyperchaotic system based on the proposed chaotic circuits, where the chaotic communication system is constituted by a chaotic transmitter and a chaotic receiver. To achieve the synchronization between the transmitter and the receiver, we are using a suitable Lyapunov function and Lyapunov theorem to design the feedback control gain. Thus, the transmitting message masked by chaotic state in the transmitter can be guaranteed to perfectly recover in the receiver. To achieve the systems performance, some basic components containing OPA, resistor and capacitor elements are used to implement the proposed communication scheme. From the viewpoints of circuit implementation, this proposed chaotic circuit is superior to the Chua chaotic circuits. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible

A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems

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Jiming Zheng

2017-01-01

Full Text Available It is an important to achieve the hybrid synchronization of the chaotic financial system. Chaos synchronization is equivalent to the error system which is asymptotically stable. The hybrid synchronization for a class of finance chaotic systems is discussed. First, a simple single variable controller is obtained to synchronize two identical chaotic financial systems with different initial conditions. Second, a novel algorithm is proposed to determine the variables of the master system that should antisynchronize with corresponding variables of the slave system and use this algorithm to determine the corresponding variables in the chaotic financial systems. The hybrid synchronization of the chaotic financial systems is realized by a simple controller. At the same time, different controllers can implement the chaotic financial system hybrid synchronization. In comparison with the existing results, the obtained controllers in this paper are simpler than those of the existing results. Finally, numerical simulations show the effectiveness of the proposed results.

Adaptive control of chaotic continuous-time systems with delay

Science.gov (United States)

Tian, Yu-Chu; Gao, Furong

1998-06-01

A simple delay system governed by a first-order differential-delay equation may behave chaotically, but the conditions for the system to have such behaviors have not been well recognized. In this paper, a set of rules is postulated first for the conditions for the delay system to display chaos. A model-reference adaptive control scheme is then proposed to control the chaotic system state to converge to an arbitrarily given reference trajectory with certain and uncertain system parameters. Numerical examples are given to analyze the chaotic behaviors of the delay system and to demonstrate the effectiveness of the proposed adaptive control scheme.

Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

International Nuclear Information System (INIS)

Dong En-Zeng; Chen Zeng-Qiang; Chen Zai-Ping; Ni Jian-Yun

2012-01-01

In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic attractor in wide parameters regions. By using the center manifold theorem and the local bifurcation theory, a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point. Numerical analysis demonstrates that the hyper-chaotic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-chaotic system is useful in the secure communication. (general)

Jamming and chaotic dynamics in different granular systems

Science.gov (United States)

Maghsoodi, Homayoon; Luijten, Erik

Although common in nature and industry, the jamming transition has long eluded a concrete, mechanistic explanation. Recently, Banigan et al. (Nat. Phys. 9, 288-292, 2013) proposed a method for characterizing this transition in a granular system in terms of the system's chaotic properties, as quantified by the largest Lyapunov exponent. They demonstrated that in a two-dimensional shear cell the jamming transition coincides with the bulk density at which the system's largest Lyapunov exponent changes sign, indicating a transition between chaotic and non-chaotic regimes. To examine the applicability of this observation to realistic granular systems, we study a model that includes frictional forces within an expanded phase space. Furthermore, we test the generality of the relation between chaos and jamming by investigating the relationship between jamming and the chaotic properties of several other granular systems, notably sheared systems (Howell, D., Behringer R. P., Veje C., Phys. Rev. Lett. 82, 5241-5244, 1999) and systems with a free boundary. Finally, we quantify correlations between the largest Lyapunov vector and collective rearrangements of the system to demonstrate the predictive capabilities enabled by adopting this perspective of jamming.

Global chaos synchronization of new chaotic systems via nonlinear control

International Nuclear Information System (INIS)

Chen, H.-K.

2005-01-01

Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach

Control of chaotic vibration in automotive wiper systems

International Nuclear Information System (INIS)

Wang Zheng; Chau, K.T.

2009-01-01

Chaotic vibration has been identified in the automotive wiper system at certain wiping speeds. This irregular vibration not only decreases the wiping efficiency, but also degrades the driving comfort. The purpose of this paper is to propose a new approach to stabilize the chaotic vibration in the wiper system. The key is to employ the extended time-delay feedback control in such a way that the applied voltage of the wiper motor is online adjusted according to its armature current feedback. Based on a practical wiper system, it is verified that the proposed approach can successfully stabilize the chaotic vibration, and provide a wide range of wiping speeds

A combination chaotic system and application in color image encryption

Science.gov (United States)

Parvaz, R.; Zarebnia, M.

2018-05-01

In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.

Spectral statistics of chaotic many-body systems

International Nuclear Information System (INIS)

Dubertrand, Rémy; Müller, Sebastian

2016-01-01

We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (paper)

Towards generalized synchronization of strictly different chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Femat, R. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Apdo. Postal 3-90, 78291 Tangamanga, San Luis Potosi S.L.P. (Mexico)]. E-mail: rfemat@ipicyt.edu.mx; Kocarev, L. [Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402 (United States)]. E-mail: lkocarev@ucsd.edu; Gerven, L. van [Department of Mechanical Engineering, Technische Universiteit Eindhoven (Netherlands); Monsivais-Perez, M.E. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Camino a la Presa San Jose 2055, 78216 Lomas 4a Sec., San Luis Potosi S.L.P. (Mexico)

2005-07-11

This contribution addresses the problem of the generalized synchronization (GS) in different chaotic systems, and departs from chaotic systems in a triangular from, which can be derived from Lie derivatives. A state-feedback (full knowledge of both master and slave systems) scheme is designed, which achieves GS. The work includes illustrative examples; moreover an experimental setup is used to corroborate the obtained results.

Generation of multi-wing chaotic attractor in fractional order system

International Nuclear Information System (INIS)

Zhang Chaoxia; Yu Simin

2011-01-01

Highlights: → We investigate a novel approach for generating multi-wing chaotic attractors. → We introduce a fundamental fractional differential nominal linear system. → A proper nonlinear state feedback controller is designed. → The controlled system can generate fractional-order multi-wing chaotic attractors. - Abstract: In this paper, a novel approach is proposed for generating multi-wing chaotic attractors from the fractional linear differential system via nonlinear state feedback controller equipped with a duality-symmetric multi-segment quadratic function. The main idea is to design a proper nonlinear state feedback controller by using four construction criterions from a fundamental fractional differential nominal linear system, so that the controlled fractional differential system can generate multi-wing chaotic attractors. It is the first time in the literature to report the multi-wing chaotic attractors from an uncoupled fractional differential system. Furthermore, some basic dynamical analysis and numerical simulations are also given, confirming the effectiveness of the proposed method.

Chaos synchronization of a unified chaotic system via partial linearization

International Nuclear Information System (INIS)

Yu Yongguang; Li Hanxiong; Duan Jian

2009-01-01

A partial linearization method is proposed for realizing the chaos synchronization of an unified chaotic system. Through synchronizing partial state of the chaotic systems can result in the synchronization of their entire states, and the resulting controller is singularity free. The results can be easily extended to the synchronization of other similar chaotic systems. Simulation results are conducted to show the effectiveness of the method.

Repetitive learning control of continuous chaotic systems

International Nuclear Information System (INIS)

Chen Maoyin; Shang Yun; Zhou Donghua

2004-01-01

Combining a shift method and the repetitive learning strategy, a repetitive learning controller is proposed to stabilize unstable periodic orbits (UPOs) within chaotic attractors in the sense of least mean square. If nonlinear parts in chaotic systems satisfy Lipschitz condition, the proposed controller can be simplified into a simple proportional repetitive learning controller

Importance sampling of rare events in chaotic systems

DEFF Research Database (Denmark)

Leitão, Jorge C.; Parente Lopes, João M.Viana; Altmann, Eduardo G.

2017-01-01

space of chaotic systems. As examples of our general framework we compute the distribution of finite-time Lyapunov exponents (in different chaotic maps) and the distribution of escape times (in transient-chaos problems). Our methods sample exponentially rare states in polynomial number of samples (in......Finding and sampling rare trajectories in dynamical systems is a difficult computational task underlying numerous problems and applications. In this paper we show how to construct Metropolis-Hastings Monte-Carlo methods that can efficiently sample rare trajectories in the (extremely rough) phase...... both low- and high-dimensional systems). An open-source software that implements our algorithms and reproduces our results can be found in reference [J. Leitao, A library to sample chaotic systems, 2017, https://github.com/jorgecarleitao/chaospp]....

Nonlinear observer based phase synchronization of chaotic systems

International Nuclear Information System (INIS)

Meng Juan; Wang Xingyuan

2007-01-01

This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme

Synchronization Between Two Different Switched Chaotic Systems By Switching Control

Directory of Open Access Journals (Sweden)

Du Li Ming

2016-01-01

Full Text Available This paper is concerned with the synchronization problem of two different switched chaotic systems, considering the general case that the master-slave switched chaotic systems have uncertainties. Two basic problems are considered: one is projective synchronization of switched chaotic systems under arbitrary switching; the other is projective synchronization of switched chaotic systems by design of switching when synchronization cannot achieved by using any subsystems alone. For the two problems, common Lyapunov function method and multiple Lyapunov function method are used respectively, an adaptive control scheme has been presented, some sufficient synchronization conditions are attainted, and the switching signal is designed. Finally, the numerical simulation is provide to show the effectiveness of our method.

Adaptive control of discrete-time chaotic systems: a fuzzy control approach

International Nuclear Information System (INIS)

Feng Gang; Chen Guanrong

2005-01-01

This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T-S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm

Improvement on generalised synchronisation of chaotic systems

International Nuclear Information System (INIS)

Hui-Bin, Zhu; Fang, Qiu; Bao-Tong, Cui

2010-01-01

In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis

Lectures on chaotic dynamical systems

CERN Document Server

Afraimovich, Valentin

2002-01-01

This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.

Lag synchronization of chaotic systems with time-delayed linear

Indian Academy of Sciences (India)

In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.

Security analysis of chaotic communication systems based on Volterra-Wiener-Korenberg model

International Nuclear Information System (INIS)

Lei Min; Meng Guang; Feng Zhengjin

2006-01-01

Pseudo-randomicity is an important cryptological characteristic for proof of encryption algorithms. This paper proposes a nonlinear detecting method based on Volterra-Wiener-Korenberg model and suggests an autocorrelation function to analyze the pseudo-randomicity of chaotic secure systems under different sampling interval. The results show that: (1) the increase of the order of the chaotic transmitter will not necessarily result in a high degree of security; (2) chaotic secure systems have higher and stronger pseudo-randomicity at sparse sampling interval due to the similarity of chaotic time series to the noise; (3) Volterra-Wiener-Korenberg method can also give a further appropriate sparse sampling interval for improving the security of chaotic secure communication systems. For unmasking chaotic communication systems, the Volterra-Wiener-Korenberg technique can be applied to analyze the chaotic time series with surrogate data

Bifurcation Control of Chaotic Dynamical Systems

National Research Council Canada - National Science Library

Wang, Hua O; Abed, Eyad H

1992-01-01

A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...

A stream cipher based on a spatiotemporal chaotic system

International Nuclear Information System (INIS)

Li Ping; Li Zhong; Halang, Wolfgang A.; Chen Guanrong

2007-01-01

A stream cipher based on a spatiotemporal chaotic system is proposed. A one-way coupled map lattice consisting of logistic maps is served as the spatiotemporal chaotic system. Multiple keystreams are generated from the coupled map lattice by using simple algebraic computations, and then are used to encrypt plaintext via bitwise XOR. These make the cipher rather simple and efficient. Numerical investigation shows that the cryptographic properties of the generated keystream are satisfactory. The cipher seems to have higher security, higher efficiency and lower computation expense than the stream cipher based on a spatiotemporal chaotic system proposed recently

Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

Directory of Open Access Journals (Sweden)

Vaidyanathan Sundarapandian

2015-09-01

Full Text Available First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1 = 0.0395,L2 = 0 and L3 = −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY =3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

Fuzzy model-based adaptive synchronization of time-delayed chaotic systems

International Nuclear Information System (INIS)

Vasegh, Nastaran; Majd, Vahid Johari

2009-01-01

In this paper, fuzzy model-based synchronization of a class of first order chaotic systems described by delayed-differential equations is addressed. To design the fuzzy controller, the chaotic system is modeled by Takagi-Sugeno fuzzy system considering the properties of the nonlinear part of the system. Assuming that the parameters of the chaotic system are unknown, an adaptive law is derived to estimate these unknown parameters, and the stability of error dynamics is guaranteed by Lyapunov theory. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.

Encryption in Chaotic Systems with Sinusoidal Excitations

Directory of Open Access Journals (Sweden)

G. Obregón-Pulido

2014-01-01

Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.

On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization

International Nuclear Information System (INIS)

Lu Zhao; Shieh Leangsan; Chen GuanRong

2003-01-01

This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen's system illustrate the effectiveness of the proposed approach

On analytical justification of phase synchronization in different chaotic systems

International Nuclear Information System (INIS)

Erjaee, G.H.

2009-01-01

In analytical or numerical synchronizations studies of coupled chaotic systems the phase synchronizations have less considered in the leading literatures. This article is an attempt to find a sufficient analytical condition for stability of phase synchronization in some coupled chaotic systems. The method of nonlinear feedback function and the scheme of matrix measure have been used to justify this analytical stability, and tested numerically for the existence of the phase synchronization in some coupled chaotic systems.

Experimental chaotic quantification in bistable vortex induced vibration systems

Science.gov (United States)

Huynh, B. H.; Tjahjowidodo, T.

2017-02-01

The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear

Generation and control of multi-scroll chaotic attractors in fractional order systems

International Nuclear Information System (INIS)

Ahmad, Wajdi M.

2005-01-01

The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations

Shape synchronization control for three-dimensional chaotic systems

International Nuclear Information System (INIS)

Huang, Yuanyuan; Wang, Yinhe; Chen, Haoguang; Zhang, Siying

2016-01-01

This paper aims to the three-dimensional continuous chaotic system and shape of the chaotic attractor by utilizing the basic theory of plane curves in classical differential geometry, the continuous controller is synthesized for the master–slave synchronization in shape. This means that the slave system can possess the same shape of state trajectory with the master system via the continuous controller. The continuous controller is composed of three sub-controllers, which respectively correspond to the master–slave synchronization in shape for the three projective curves of the chaotic attractor onto the three coordinate planes. Moreover, the proposed shape synchronization technique as well as application of control scheme to secure communication is also demonstrated in this paper, where numerical simulation results show the proposed control method works well.

Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems

Directory of Open Access Journals (Sweden)

Cuimei Jiang

2015-07-01

Full Text Available Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes.

Controlling chaotic and hyperchaotic systems via energy regulation

International Nuclear Information System (INIS)

Laval, L.; M'Sirdi, N.K.

2003-01-01

This paper focuses on a new control approach to steer trajectories of chaotic or hyperchaotic systems towards stable periodic orbits or stationary points of interest. This approach mainly consists in a variable structure control (VSC) that we extend by explicitly considering the system energy as basis for both controller design and system stabilization. In this paper, we present some theoretical results for a class of nonlinear (possibly chaotic or hyperchaotic) systems. Then some capabilities of the proposed approach are illustrated through examples related to a four-dimensional hyperchaotic system

Synchronization of a unified chaotic system and the application in secure communication

International Nuclear Information System (INIS)

Lu Junan; Wu Xiaoqun; Lue Jinhu

2002-01-01

This Letter further investigates the synchronization of a unified chaotic system via different methods. Several sufficient theorems for the synchronization of the unified chaotic system are deduced. A scheme of secure communication based on the synchronization of the unified chaotic system is presented. Numerical simulation shows its feasibility

Synchronization of the unified chaotic systems using a sliding mode controller

International Nuclear Information System (INIS)

Zribi, Mohamed; Smaoui, Nejib; Salim, Haitham

2009-01-01

The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lue chaotic systems. This paper deals with the synchronization of two identical unified chaotic systems where the slave system is assumed to have a single input. A sliding mode controller is proposed to synchronize the two systems. The asymptotic convergence to zero of the errors between the states of the master and the slave systems is shown. Simulations results are presented to illustrate the proposed controller; they indicate that the designed controller is able to synchronize the unified chaotic systems. Also, simulation results show that the proposed control scheme is robust to random bounded disturbances acting on the master system. Moreover, the proposed scheme is applied to the secure communications field, where simulation results indicate that the proposed scheme is effective.

Estimating parameters of chaotic systems synchronized by external driving signal

International Nuclear Information System (INIS)

Wu Xiaogang; Wang Zuxi

2007-01-01

Noise-induced synchronization (NIS) has evoked great research interests recently. Two uncoupled identical chaotic systems can achieve complete synchronization (CS) by feeding a common noise with appropriate intensity. Actually, NIS belongs to the category of external feedback control (EFC). The significance of applying EFC in secure communication lies in fact that the trajectory of chaotic systems is disturbed so strongly by external driving signal that phase space reconstruction attack fails. In this paper, however, we propose an approach that can accurately estimate the parameters of the chaotic systems synchronized by external driving signal through chaotic transmitted signal, driving signal and their derivatives. Numerical simulation indicates that this approach can estimate system parameters and external coupling strength under two driving modes in a very rapid manner, which implies that EFC is not superior to other methods in secure communication

Modelling of long-wave chaotic radar system for anti-stealth applications

Science.gov (United States)

Al-Suhail, Ghaida A.; Tahir, Fadhil Rahma; Abd, Mariam Hussien; Pham, Viet-Thanh; Fortuna, Luigi

2018-04-01

Although the Very Low-Frequency (VLF) waveforms have limited practical applications in acoustics (sonar) and secure military communications with radars and submarines; to this end; this paper presents a new and simple analytical model of VLF monostatic direct chaotic radar system. The model hypothetically depends on the two identical coupled time-delayed feedback chaotic systems which can generate and recover a long-wave chaotic signal. To resist the influence of positive Lyapunov exponents of the time-delay chaotic systems, the complete replacement of Pecaro and Carroll (PC) synchronization is employed. It can faithfully recover the chaotic signal from the back-scattered (echo) signal from the target over a noisy channel. The system performance is characterized in terms of the time series of synchronization in addition to the peak of the cross-correlation. Simulation results are conducted for substantial sensitivities of the chaotic signal to the system parameters and initial conditions. As a result, it is found that an effective and robust chaotic radar (CRADAR) model can be obtained when the signal-to-noise ratio (SNR) highly degrades to 0 dB, but with clear peak in correlation performance for detecting the target. Then, the model can be considered as a state of the art towards counter stealth technology and might be developed for other acoustic secure applications.

Designing synchronization schemes for chaotic fractional-order unified systems

International Nuclear Information System (INIS)

Wang Junwei; Zhang Yanbin

2006-01-01

Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration

Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

Directory of Open Access Journals (Sweden)

M. S. H. Chowdhury

2012-01-01

Full Text Available Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4 solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.

CMAC-based adaptive backstepping synchronization of uncertain chaotic systems

International Nuclear Information System (INIS)

Lin, C.-M.; Peng, Y.-F.; Lin, M.-H.

2009-01-01

This study proposes an adaptive backstepping control system for synchronizing uncertain chaotic system by using cerebellar model articulation controller (CMAC). CMAC is a nonlinear network with simple computation, good generalization capability and fast learning property. The proposed CMAC-based adaptive backstepping control (CABC) system uses backstepping method and adaptive cerebellar model articulation controller (ACMAC) for synchronizing uncertain chaotic system. Finally, simulation results for the Genesio system are presented to illustrate the effectiveness of the proposed control system.

Observer based on sliding mode variable structure for synchronization of chaotic systems

International Nuclear Information System (INIS)

Yin Xunhe; Shan Xiuming; Ren Yong

2003-01-01

In the paper an approach, based on the state observer of sliding mode variable structure, is used for synchronizing chaotic systems. It does not require either the computation of the Lyapunov exponents, or the initial conditions belonging to the same basin of attraction as the existed approaches based on the state observer for synchronizing chaotic systems. The approach is more robust against noise and parameter mismatch than the existed approaches based on the state observer for synchronizing chaotic systems, because the former uses variable structure control, which is strong robust with respect to noise and parameter mismatch in the error dynamics, the later uses an appropriate choice of the feedback gain. Two well-known chaotic systems, a chaotic Roessler system and a hyperchaotic Roessler system are considered as illustrative examples to demonstrate the effectiveness of the used approach by numerical simulations

Adaptive observer based synchronization of a class of uncertain chaotic systems

International Nuclear Information System (INIS)

Bowong, S.; Yamapi, R.

2005-05-01

This study addresses the adaptive synchronization of a class of uncertain chaotic systems in the drive-response framework. For a class of uncertain chaotic systems with unknown parameters and external disturbances, a robust adaptive observer based response system is constructed to synchronize the uncertain chaotic system. Lyapunov stability theory and Barbalat lemma ensure the global synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of the Genesio-Tesi system verifies the effectiveness of the proposed method. (author)

On nonlinear control design for autonomous chaotic systems of integer and fractional orders

International Nuclear Information System (INIS)

Ahmad, Wajdi M.; Harb, Ahmad M.

2003-01-01

In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

Science.gov (United States)

Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

2018-02-01

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

A numeric-analytic method for approximating the chaotic Chen system

International Nuclear Information System (INIS)

Mossa Al-sawalha, M.; Noorani, M.S.M.

2009-01-01

The epitome of this paper centers on the application of the differential transformation method (DTM) the renowned Chen system which is described as a three-dimensional system of ODEs with quadratic nonlinearities. Numerical comparisons are made between the DTM and the classical fourth-order Runge-Kutta method (RK4). Our work showcases the precision of the DTM as the Chen system transforms from a non-chaotic system to a chaotic one. Since the Lyapunov exponent for this system is much higher compared to other chaotic systems, we shall highlight the difficulties of the simulations with respect to its accuracy. We wrap up our investigations to reveal that this direct symbolic-numeric scheme is effective and accurate.

A simple observer of the generalized Chen chaotic systems

International Nuclear Information System (INIS)

Sun, Y.-J.

2009-01-01

In this paper, the generalized Chen chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Chen chaotic system is proposed to guarantee the global exponential stability of the resulting error system. Furthermore, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is provided to illustrate the use of the main result.

Aging in a Chaotic System

OpenAIRE

Barkai, E.

2002-01-01

We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks, introduced previously to model diffusion in glasses.

A novel grid multiwing chaotic system with only non-hyperbolic equilibria

Science.gov (United States)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-05-01

The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.

Chaos synchronization of a new chaotic system via nonlinear control

International Nuclear Information System (INIS)

Zhang Qunjiao; Lu Junan

2008-01-01

This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

Constructing a one-way hash function based on the unified chaotic system

International Nuclear Information System (INIS)

Long Min; Peng Fei; Chen Guanrong

2008-01-01

A new one-way hash function based on the unified chaotic system is constructed. With different values of a key parameter, the unified chaotic system represents different chaotic systems, based on which the one-way hash function algorithm is constructed with three round operations and an initial vector on an input message. In each round operation, the parameters are processed by three different chaotic systems generated from the unified chaotic system. Feed-forwards are used at the end of each round operation and at the end of each element of the message processing. Meanwhile, in each round operation, parameter-exchanging operations are implemented. Then, the hash value of length 160 bits is obtained from the last six parameters. Simulation and analysis both demonstrate that the algorithm has great flexibility, satisfactory hash performance, weak collision property, and high security. (general)

Stabilization at almost arbitrary points for chaotic systems

International Nuclear Information System (INIS)

Huang, C.-S.; Lian, K.-Y.; Su, C.-H.; Wu, J.-W.

2008-01-01

We consider how to design a feasible control input for chaotic systems via a suitable input channel to achieve the stabilization at arbitrary points. Regarding the nonlinear systems without naturally defined input vectors, we propose a local stabilization controller which works for almost arbitrary points. Subsequently, according to topologically transitive property for chaotic systems, the feedback control force is activated only when the trajectory passes through the neighboring region of the regulated point. Hence the global stabilization is achieved whereas the control effort of the hybrid controller is extremely low

Modification for collection of master-slave synchronized chaotic systems

International Nuclear Information System (INIS)

Guo Rongwei; Li Gang

2009-01-01

In this paper, based on the adaptive-feedback control method, we synchronize two identical chaotic systems. In comparison with the previous methods such as the open-plus-closed-loop (OPCL) method, the present control scheme is simple, and therefore it is easily implemented in practice. At last, a group of chaotic systems are used to demonstrate the effectiveness of this method.

An exponential observer for the generalized Rossler chaotic system

International Nuclear Information System (INIS)

Sun, Y.-J.

2009-01-01

In this paper, the generalized Rossler chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a state observer for the generalized Rossler chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be arbitrarily pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.

Optimal Control for a Class of Chaotic Systems

Directory of Open Access Journals (Sweden)

Jianxiong Zhang

2012-01-01

Full Text Available This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs. In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP. Finally, numerical examples are given to illustrate the results.

Extreme multistability in a memristor-based multi-scroll hyper-chaotic system

Energy Technology Data Exchange (ETDEWEB)

Yuan, Fang, E-mail: yf210yf@163.com; Wang, Guangyi, E-mail: wanggyi@163.com [Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018 (China); Wang, Xiaowei [Department of Automation, Shanghai University, Shanghai 200072 (China)

2016-07-15

In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

Extreme multistability in a memristor-based multi-scroll hyper-chaotic system.

Science.gov (United States)

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2016-07-01

In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

Synchronization of two chaotic systems: Dynamic compensator approach

International Nuclear Information System (INIS)

Chen, C.-K.; Lai, T.-W.; Yan, J.-J.; Liao, T.-L.

2009-01-01

This study is concerned with the identical synchronization problem for a class of chaotic systems. A dynamic compensator is proposed to achieve the synchronization between master and slave chaotic systems using only the accessible output variables. A sufficient condition is also proposed to ensure the global synchronization. Furthermore, the strictly positive real (SPR) restriction, which is normally required in most of the observer-based synchronization schemes, is released in our approach. Two numerical examples are included to illustrate the proposed scheme.

Adaptive fuzzy observer based synchronization design and secure communications of chaotic systems

International Nuclear Information System (INIS)

Hyun, Chang-Ho; Kim, Jae-Hun; Kim, Euntai; Park, Mignon

2006-01-01

This paper proposes a synchronization design scheme based on an alternative indirect adaptive fuzzy observer and its application to secure communication of chaotic systems. It is assumed that their states are unmeasurable and their parameters are unknown. Chaotic systems and the structure of the fuzzy observer are represented by the Takagi-Sugeno fuzzy model. Using Lyapunov stability theory, an adaptive law is derived to estimate the unknown parameters and the stability of the proposed system is guaranteed. Through this process, the asymptotic synchronization of chaotic systems is achieved. The proposed observer is applied to secure communications of chaotic systems and some numerical simulation results show the validity of theoretical derivations and the performance of the proposed observer

Estimating the state of large spatio-temporally chaotic systems

International Nuclear Information System (INIS)

Ott, E.; Hunt, B.R.; Szunyogh, I.; Zimin, A.V.; Kostelich, E.J.; Corazza, M.; Kalnay, E.; Patil, D.J.; Yorke, J.A.

2004-01-01

We consider the estimation of the state of a large spatio-temporally chaotic system from noisy observations and knowledge of a system model. Standard state estimation techniques using the Kalman filter approach are not computationally feasible for systems with very many effective degrees of freedom. We present and test a new technique (called a Local Ensemble Kalman Filter), generally applicable to large spatio-temporally chaotic systems for which correlations between system variables evaluated at different points become small at large separation between the points

Applications of modularized circuit designs in a new hyper-chaotic system circuit implementation

International Nuclear Information System (INIS)

Wang Rui; Sun Hui; Wang Jie-Zhi; Wang Lu; Wang Yan-Chao

2015-01-01

Modularized circuit designs for chaotic systems are introduced in this paper. Especially, a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation. In this paper, the detailed design procedures are described. Multisim simulations and physical experiments are conducted, and the simulation results are compared with Matlab simulation results for different system parameter pairs. These results are consistent with each other and they verify the existence of the hyper-chaotic attractor for this new hyper-chaotic system. (paper)

Modeling of Some Chaotic Systems with AnyLogic Software

Directory of Open Access Journals (Sweden)

Biljana Zlatanovska

2018-05-01

Full Text Available The chaotic systems are already known in the theory of chaos. In our paper will be analyzed the following chaotic systems: Rossler, Chua and Chen systems. All of them are systems of ordinary differential equations. By mathematical software Mathematica and MatLab, their graphical representation as continuous dynamical systems is already known. By computer simulations, via examples, the systems will be analyzed using AnyLogic software. We would like to present the way how ordinary differential equations are modeling with AnyLogic software, as one of the simplest software for use.

Chaotic Secure Communication Systems with an Adaptive State Observer

Directory of Open Access Journals (Sweden)

Wei-Der Chang

2015-01-01

Full Text Available This paper develops a new digital communication scheme based on using a unified chaotic system and an adaptive state observer. The proposed communication system basically consists of five important elements: signal modulation, chaotic encryption, adaptive state observer, chaotic decryption, and signal demodulation. A sequence of digital signals will be delivered from the transmitter to the receiver through a public channel. It is rather reasonable that if the number of signals delivered on the public channel is fewer, then the security of such communication system is more guaranteed. Therefore, in order to achieve this purpose, a state observer will be designed and its function is to estimate full system states only by using the system output signals. In this way, the signals delivered on the public channel can be reduced mostly. According to these estimated state signals, the original digital sequences are then retrieved completely. Finally, experiment results are provided to verify the applicability of the proposed communication system.

Chaos synchronization of a chaotic system via nonlinear control

International Nuclear Information System (INIS)

Park, Ju H.

2005-01-01

In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

A novel four-wing non-equilibrium chaotic system and its circuit ...

Indian Academy of Sciences (India)

Abstract. In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilib- ria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and ...

Adaptive control of chaotic systems with stochastic time varying unknown parameters

Energy Technology Data Exchange (ETDEWEB)

Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu

2008-10-15

In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment.

Robust networked H∞ synchronization of nonidentical chaotic Lur'e systems

International Nuclear Information System (INIS)

Yang De-Dong

2014-01-01

We mainly investigate the robust networked H ∞ synchronization problem of nonidentical chaotic Lur'e systems. In the design of the synchronization scheme, some network characteristics, such as nonuniform sampling, transmission-induced delays, and data packet dropouts, are considered. The parameters of master—slave chaotic Lur'e systems often allow differences. The sufficient condition in terms of linear matrix inequality (LMI) is obtained to guarantee the dissipative synchronization of nonidentical chaotic Lur'e systems in network environments. A numerical example is given to illustrate the validity of the proposed method. (general)

Chaos control of chaotic dynamical systems using backstepping design

International Nuclear Information System (INIS)

Yassen, M.T.

2006-01-01

This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lue systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results

Multi-machine power system stabilizers design using chaotic optimization algorithm

Energy Technology Data Exchange (ETDEWEB)

Shayeghi, H., E-mail: hshayeghi@gmail.co [Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil (Iran, Islamic Republic of); Shayanfar, H.A. [Center of Excellence for Power System Automation and Operation, Electrical Engineering Department, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Jalilzadeh, S.; Safari, A. [Technical Engineering Department, Zanjan University, Zanjan (Iran, Islamic Republic of)

2010-07-15

In this paper, a multiobjective design of the multi-machine power system stabilizers (PSSs) using chaotic optimization algorithm (COA) is proposed. Chaotic optimization algorithms, which have the features of easy implementation, short execution time and robust mechanisms of escaping from the local optimum, is a promising tool for the engineering applications. The PSSs parameters tuning problem is converted to an optimization problem which is solved by a chaotic optimization algorithm based on Lozi map. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed chaotic optimization problem introduces chaos mapping using Lozi map chaotic sequences which increases its convergence rate and resulting precision. Two different objective functions are proposed in this study for the PSSs design problem. The first objective function is the eigenvalues based comprising the damping factor, and the damping ratio of the lightly damped electro-mechanical modes, while the second is the time domain-based multi-objective function. The robustness of the proposed COA-based PSSs (COAPSS) is verified on a multi-machine power system under different operating conditions and disturbances. The results of the proposed COAPSS are demonstrated through eigenvalue analysis, nonlinear time-domain simulation and some performance indices. In addition, the potential and superiority of the proposed method over the classical approach and genetic algorithm is demonstrated.

A note on synchronization between two different chaotic systems

International Nuclear Information System (INIS)

Park, Ju H.

2009-01-01

In this paper, a new control method based on the Lyapunov method and linear matrix inequality framework is proposed to design a stabilizing controller for synchronizing two different chaotic systems. The feedback controller is consisted of two parts: linear dynamic control law and nonlinear control one. By this control law, the exponential stability for synchronization between two different chaotic systems is guaranteed. As applications of proposed method, synchronization problem between Genesio-Tesi system and Chen system has been investigated, and then the similar approach is applied to the synchronization problem between Roessler system and Lorenz system.

Parameter Identification and Synchronization of Uncertain Chaotic Systems Based on Sliding Mode Observer

Directory of Open Access Journals (Sweden)

Li-lian Huang

2013-01-01

Full Text Available The synchronization of nonlinear uncertain chaotic systems is investigated. We propose a sliding mode state observer scheme which combines the sliding mode control with observer theory and apply it into the uncertain chaotic system with unknown parameters and bounded interference. Based on Lyapunov stability theory, the constraints of synchronization and proof are given. This method not only can realize the synchronization of chaotic systems, but also identify the unknown parameters and obtain the correct parameter estimation. Otherwise, the synchronization of chaotic systems with unknown parameters and bounded external disturbances is robust by the design of the sliding surface. Finally, numerical simulations on Liu chaotic system with unknown parameters and disturbances are carried out. Simulation results show that this synchronization and parameter identification has been totally achieved and the effectiveness is verified very well.

Contraction theory based adaptive synchronization of chaotic systems

International Nuclear Information System (INIS)

Sharma, B.B.; Kar, I.N.

2009-01-01

Contraction theory based stability analysis exploits the incremental behavior of trajectories of a system with respect to each other. Application of contraction theory provides an alternative way for stability analysis of nonlinear systems. This paper considers the design of a control law for synchronization of certain class of chaotic systems based on backstepping technique. The controller is selected so as to make the error dynamics between the two systems contracting. Synchronization problem with and without uncertainty in system parameters is discussed and necessary stability proofs are worked out using contraction theory. Suitable adaptation laws for unknown parameters are proposed based on the contraction principle. The numerical simulations verify the synchronization of the chaotic systems. Also parameter estimates converge to their true values with the proposed adaptation laws.

A simple observer design of the generalized Lorenz chaotic systems

International Nuclear Information System (INIS)

Sun, Y.-J.

2010-01-01

In this Letter, the generalized Lorenz chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Lorenz chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is given to show the effectiveness of the obtained result.

Exact solutions to chaotic and stochastic systems

Science.gov (United States)

González, J. A.; Reyes, L. I.; Guerrero, L. E.

2001-03-01

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.

Global bifurcations in fractional-order chaotic systems with an extended generalized cell mapping method

Energy Technology Data Exchange (ETDEWEB)

Liu, Xiaojun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China); School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001 (China); Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn; Jiang, Jun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China)

2016-08-15

Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.

Predicting the bounds of large chaotic systems using low-dimensional manifolds.

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Asger M Haugaard

Full Text Available Predicting extrema of chaotic systems in high-dimensional phase space remains a challenge. Methods, which give extrema that are valid in the long term, have thus far been restricted to models of only a few variables. Here, a method is presented which treats extrema of chaotic systems as belonging to discretised manifolds of low dimension (low-D embedded in high-dimensional (high-D phase space. As a central feature, the method exploits that strange attractor dimension is generally much smaller than parent system phase space dimension. This is important, since the computational cost associated with discretised manifolds depends exponentially on their dimension. Thus, systems that would otherwise be associated with tremendous computational challenges, can be tackled on a laptop. As a test, bounding manifolds are calculated for high-D modifications of the canonical Duffing system. Parameters can be set such that the bounding manifold displays harmonic behaviour even if the underlying system is chaotic. Thus, solving for one post-transient forcing cycle of the bounding manifold predicts the extrema of the underlying chaotic problem indefinitely.

Synchronization and an application of a novel fractional order King Cobra chaotic system

Energy Technology Data Exchange (ETDEWEB)

Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com [Department of Mathematics, Gandhigram Rural Institute‐Deemed University, Gandhigram 624 302, Tamilnadu (India); Ratnavelu, K., E-mail: kuru052001@gmail.com [Faculty of Science, Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)

2014-09-01

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.

Hybrid synchronization of two independent chaotic systems on ...

Indian Academy of Sciences (India)

Keywords. Hybrid synchronization; complex network; information source; chaotic system. ... encryption and decryption through synchronization. However, the ... Certainly, if the two systems are different, the security would be improved. How.

Horseshoes in a Chaotic System with Only One Stable Equilibrium

Science.gov (United States)

Huan, Songmei; Li, Qingdu; Yang, Xiao-Song

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.

Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems

International Nuclear Information System (INIS)

Yau, H.-T.; Chen, C.-L.

2006-01-01

This paper proposes a chattering-free fuzzy sliding-mode control (FSMC) strategy for uncertain chaotic systems. A fuzzy logic control is used to replace the discontinuous sign function of the reaching law in traditional sliding-mode control (SMC), and hence a control input without chattering is obtained in the chaotic systems with uncertainties. Base on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding-mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. The Genesio chaotic system is used to test the proposed control strategy and the simulation results show the FSMC not only can control the uncertain chaotic behaviors to a desired state without oscillator very fast, but also the switching function is smooth without chattering. This result implies that this strategy is feasible and effective for chaos control

Security analysis of communication system based on the synchronization of different order chaotic systems

International Nuclear Information System (INIS)

Alvarez, Gonzalo; Hernandez, Luis; Munoz, Jaime; Montoya, Fausto; Li Shujun

2005-01-01

This Letter analyzes the security weakness of a recently proposed communication method based on chaotic modulation and masking using synchronization of two chaotic systems with different orders. It is shown that its application to secure communication is unsafe, because it can be broken in two different ways, by high-pass filtering and by reduced order system synchronization, without knowing neither the system parameter values nor the system key

A Retrospection of Chaotic Phenomena in Electrical Systems

Directory of Open Access Journals (Sweden)

Umesh Kumar

1998-01-01

Full Text Available In the last decade new phenomena have been observed in all areas of non linear dynamics, principal among these being ‘Chaotic phenomena’. Chaos has been reported virtually from every scientific discipline. This paper summarizes a study of the chaotic phenomena in electrical systems and attempts to translate the mathematical ideas and techniques into language that engineers and applied scientists can use to study ‘Chaos’. Towards this end, the paper has summarized the study of chaos in several examples like Chua’s circuit family; Folded Torus circuit; non-autonomous circuits; switched capacitor circuits and hyper-chaos circuits. As observed in power systems, control systems and digital filters, chaos has been exhibited and shown on examples.

Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium

Directory of Open Access Journals (Sweden)

Xiong Wang

2017-01-01

Full Text Available A system without equilibrium has been proposed in this work. Although there is an absence of equilibrium points, the system displays chaos, which has been confirmed by phase portraits and Lyapunov exponents. The system is realized on an electronic card, which exhibits chaotic signals. Furthermore, chaotic property of the system is applied in multimedia security such as image encryption and sound steganography.

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

International Nuclear Information System (INIS)

Fu Shi-Hui; Lu Qi-Shao; Du Ying

2012-01-01

Adaptive H ∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lyapunov's stability theory, linear and nonlinear feedback control of adaptive H ∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H ∞ -norm constraint. Adaptive H ∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis. (general)

Finite-time synchronization of a class of autonomous chaotic systems

Indian Academy of Sciences (India)

Some criteria for achieving the finite-time synchronization of a class of autonomous chaotic systems are derived by the finite-time stability theory and Gerschgorin disc theorem. Numerical simulations are shown to illustrate the effectiveness of the proposed method. Keywords. Finite-time synchronization; autonomous chaotic ...

Amplification through chaotic synchronization in spatially extended beam-plasma systems

Science.gov (United States)

Moskalenko, Olga I.; Frolov, Nikita S.; Koronovskii, Alexey A.; Hramov, Alexander E.

2017-12-01

In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.

An Anti-Cheating Visual Cryptography Scheme Based on Chaotic Encryption System

Science.gov (United States)

Han, Yanyan; Xu, Zhuolin; Ge, Xiaonan; He, Wencai

By chaotic encryption system and introducing the trusted third party (TTP), in this paper, an anti-cheating visual cryptography scheme (VCS) is proposed. The scheme solved the problem of dishonest participants and improved the security of chaotic encryption system. Simulation results and analysis show that the recovery image is acceptable, the system can detect the cheating in participants effectively and with high security.

Controlling chaotic systems via nonlinear feedback control

International Nuclear Information System (INIS)

Park, Ju H.

2005-01-01

In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived

Multiswitching compound antisynchronization of four chaotic systems

Indian Academy of Sciences (India)

Ayub Khan

2017-11-28

Nov 28, 2017 ... systems, electrical engineering, information process- ... model. The synchronization problem among three or more chaotic ...... we perform numerical simulations in MATLAB using ... In the simulation process we assume α1 =.

Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

Directory of Open Access Journals (Sweden)

S. Vaidyanathan

2013-09-01

Full Text Available This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B. In this work, a detailed qualitative analysis of the novel chaotic systems (A and (B has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE for the novel chaotic systems (A and (B has a large value, viz. for the system (A and for the system (B. Thus, both the novel chaotic systems (A and (B display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A, identical chaotic systems (B and nonidentical chaotic systems (A and (B with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A and (B have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A and (B, and also the adaptive synchronization results derived for the novel chaotic systems (A and (B.

Stages of chaotic synchronization.

Science.gov (United States)

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

Nonlinear PI control of chaotic systems using singular perturbation theory

International Nuclear Information System (INIS)

Wang Jiang; Wang Jing; Li Huiyan

2005-01-01

In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

Output synchronization of chaotic systems under nonvanishing perturbations

Energy Technology Data Exchange (ETDEWEB)

Lopez-Mancilla, Didier [Departamento de Ciencias Exactas y Tecnologicas, Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG), Enrique Diaz de Leon s/n, 47460 Lagos de Moreno, Jal. (Mexico)], E-mail: didier@uabc.mx; Cruz-Hernandez, Cesar [Electronics and Telecommunications Department, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107, Carretera Tijuana-Ensenada, 22860 Ensenada, B.C. (Mexico)], E-mail: ccruz@cicese.mx

2008-08-15

In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included.

Output synchronization of chaotic systems under nonvanishing perturbations

International Nuclear Information System (INIS)

Lopez-Mancilla, Didier; Cruz-Hernandez, Cesar

2008-01-01

In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included

Improving performance of DS-CDMA systems using chaotic complex Bernoulli spreading codes

Science.gov (United States)

Farzan Sabahi, Mohammad; Dehghanfard, Ali

2014-12-01

The most important goal of spreading spectrum communication system is to protect communication signals against interference and exploitation of information by unintended listeners. In fact, low probability of detection and low probability of intercept are two important parameters to increase the performance of the system. In Direct Sequence Code Division Multiple Access (DS-CDMA) systems, these properties are achieved by multiplying the data information in spreading sequences. Chaotic sequences, with their particular properties, have numerous applications in constructing spreading codes. Using one-dimensional Bernoulli chaotic sequence as spreading code is proposed in literature previously. The main feature of this sequence is its negative auto-correlation at lag of 1, which with proper design, leads to increase in efficiency of the communication system based on these codes. On the other hand, employing the complex chaotic sequences as spreading sequence also has been discussed in several papers. In this paper, use of two-dimensional Bernoulli chaotic sequences is proposed as spreading codes. The performance of a multi-user synchronous and asynchronous DS-CDMA system will be evaluated by applying these sequences under Additive White Gaussian Noise (AWGN) and fading channel. Simulation results indicate improvement of the performance in comparison with conventional spreading codes like Gold codes as well as similar complex chaotic spreading sequences. Similar to one-dimensional Bernoulli chaotic sequences, the proposed sequences also have negative auto-correlation. Besides, construction of complex sequences with lower average cross-correlation is possible with the proposed method.

Identification of chaotic memristor systems based on piecewise adaptive Legendre filters

International Nuclear Information System (INIS)

Zhao, Yibo; Zhang, Xiuzai; Xu, Jin; Guo, Yecai

2015-01-01

Memristor is a nonlinear device, which plays an important role in the design and implementation of chaotic systems. In order to be able to understand in-depth the complex nonlinear dynamic behaviors in chaotic memristor systems, modeling or identification of its nonlinear model is very important premise. This paper presents a chaotic memristor system identification method based on piecewise adaptive Legendre filters. The threshold decomposition is carried out for the input vector, and also the input signal subintervals via decomposition satisfy the convergence condition of the adaptive Legendre filters. Then the adaptive Legendre filter structure and adaptive weight update algorithm are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics.

Chaotic System Identification Based on a Fuzzy Wiener Model with Particle Swarm Optimization

International Nuclear Information System (INIS)

Yong, Li; Ying-Gan, Tang

2010-01-01

A fuzzy Wiener model is proposed to identify chaotic systems. The proposed fuzzy Wiener model consists of two parts, one is a linear dynamic subsystem and the other is a static nonlinear part, which is represented by the Takagi–Sugeno fuzzy model. Identification of chaotic systems is converted to find optimal parameters of the fuzzy Wiener model by minimizing the state error between the original chaotic system and the fuzzy Wiener model. Particle swarm optimization algorithm, a global optimizer, is used to search the optimal parameter of the fuzzy Wiener model. The proposed method can identify the parameters of the linear part and nonlinear part simultaneously. Numerical simulations for Henón and Lozi chaotic system identification show the effectiveness of the proposed method

Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems

Directory of Open Access Journals (Sweden)

Roman Senkerik

2014-01-01

Full Text Available Evolutionary technique differential evolution (DE is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.

Generalized projective synchronization of chaotic systems via adaptive learning control

International Nuclear Information System (INIS)

Yun-Ping, Sun; Jun-Min, Li; Hui-Lin, Wang; Jiang-An, Wang

2010-01-01

In this paper, a learning control approach is applied to the generalized projective synchronisation (GPS) of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov–Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme. (general)

Directing orbits of chaotic systems by particle swarm optimization

International Nuclear Information System (INIS)

Liu Bo; Wang Ling; Jin Yihui; Tang Fang; Huang Dexian

2006-01-01

This paper applies a novel evolutionary computation algorithm named particle swarm optimization (PSO) to direct the orbits of discrete chaotic dynamical systems towards desired target region within a short time by adding only small bounded perturbations, which could be formulated as a multi-modal numerical optimization problem with high dimension. Moreover, the synchronization of chaotic systems is also studied, which can be dealt with as an online problem of directing orbits. Numerical simulations based on Henon Map demonstrate the effectiveness and efficiency of PSO, and the effects of some parameters are also investigated

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

Science.gov (United States)

Wang, Rong; Gao, Jin-Yue

2005-09-01

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

Study of chaos in chaotic satellite systems

Indian Academy of Sciences (India)

Lyapunov exponents are estimated. From these studies, chaosin satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the ...

Robust control of time-delay chaotic systems

International Nuclear Information System (INIS)

Hua Changchun; Guan Xinping

2003-01-01

Robust control problem of nonlinear time-delay chaotic systems is investigated. For such uncertain systems, we propose adaptive feedback controller and novel nonlinear feedback controller. They are both independent of the time delay and can render the corresponding closed-loop systems globally uniformly ultimately bounded stable. The simulations on controlling logistic system are made and the results show the controllers are feasible

A new chaotic cryptosystem

International Nuclear Information System (INIS)

Wei Jun; Liao Xiaofeng; Wong, Kwok-wo; Xiang Tao

2006-01-01

Based on the study of some previously proposed chaotic encryption algorithms, we found that it is dangerous to mix chaotic state or iteration number of the chaotic system with ciphertext. In this paper, a new chaotic cryptosystem is proposed. Instead of simply mixing the chaotic signal of the proposed chaotic cryptosystem with the ciphertext, a noise-like variable is utilized to govern the encryption and decryption processes. This adds statistical sense to the new cryptosystem. Numerical simulations show that the new cryptosystem is practical whenever efficiency, ciphertext length or security is concerned

Collection of master-slave synchronized chaotic systems

NARCIS (Netherlands)

Lerescu, AI; Constandache, N; Oancea, S; Grosu, [No Value

2004-01-01

In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the

Entanglement production in quantized chaotic systems

Indian Academy of Sciences (India)

Abstract. Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical ...

Entanglement production in quantized chaotic systems

Indian Academy of Sciences (India)

Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies.

H∞ synchronization of chaotic systems via dynamic feedback approach

International Nuclear Information System (INIS)

Lee, S.M.; Ji, D.H.; Park, Ju H.; Won, S.C.

2008-01-01

This Letter considers H ∞ synchronization of a general class 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 master and slave systems but also reduce the effect of external disturbance to an H ∞ norm constraint. A dynamic feedback control scheme is proposed for H ∞ synchronization in chaotic systems for the first time. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme

A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos

Directory of Open Access Journals (Sweden)

Shiyun Shen

2017-01-01

Full Text Available One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.

A novel secret image sharing scheme based on chaotic system

Science.gov (United States)

Li, Li; Abd El-Latif, Ahmed A.; Wang, Chuanjun; Li, Qiong; Niu, Xiamu

2012-04-01

In this paper, we propose a new secret image sharing scheme based on chaotic system and Shamir's method. The new scheme protects the shadow images with confidentiality and loss-tolerance simultaneously. In the new scheme, we generate the key sequence based on chaotic system and then encrypt the original image during the sharing phase. Experimental results and analysis of the proposed scheme demonstrate a better performance than other schemes and confirm a high probability to resist brute force attack.

Partial synchronization and spontaneous spatial ordering in coupled chaotic systems

International Nuclear Information System (INIS)

Ying Zhang; Gang Hu; Cerdeira, Hilda A.; Shigang Chen; Braun, Thomas; Yugui Yao

2000-11-01

A model of many symmetrically and locally coupled chaotic oscillators is studied. Partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated. Very rich patterns of the system are revealed, based on partial synchronization analysis. The stabilities of different partially synchronous spatiotemporal structures and some novel dynamical behaviors of these states are discussed both numerically and analytically. (author)

Symplectic Synchronization of Lorenz-Stenflo System with Uncertain Chaotic Parameters via Adaptive Control

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Cheng-Hsiung Yang

2013-01-01

Full Text Available A new symplectic chaos synchronization of chaotic systems with uncertain chaotic parameters is studied. The traditional chaos synchronizations are special cases of the symplectic chaos synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics and a parameter difference. The symplectic chaos synchronization with uncertain chaotic parameters may be applied to the design of secure communication systems. Finally, numerical results are studied for symplectic chaos synchronized from two identical Lorenz-Stenflo systems in three different cases.

An Eight-Term Novel Four-Scroll Chaotic System with Cubic Nonlinearity and its Circuit Simulation

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S. Sampath

2014-11-01

Full Text Available This research work proposes an eight-term novel four-scroll chaotic system with cubic nonlinearity and analyses its fundamental properties such as dissipativity, equilibria, symmetry and invariance, Lyapunov exponents and KaplanYorke dimension. The phase portraits of the novel chaotic system, which are obtained in this work by using MATLAB, depict the four-scroll attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel four-scroll chaotic system are obtained as L1 = 0.75335, L2 = 0 and L3 = −22.43304. Also, the Kaplan-Yorke dimension of the novel four-scroll chaotic system is obtained as DKY = 2.0336. Finally, an electronic circuit realization of the novel four-scroll chaotic system is presented by using SPICE to confirm the feasibility of the theoretical model.

Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach

International Nuclear Information System (INIS)

Santos Coelho, Leandro dos

2009-01-01

Despite the popularity, the tuning aspect of proportional-integral-derivative (PID) controllers is a challenge for researchers and plant operators. Various controllers tuning methodologies have been proposed in the literature such as auto-tuning, self-tuning, pattern recognition, artificial intelligence, and optimization methods. Chaotic optimization algorithms as an emergent method of global optimization have attracted much attention in engineering applications. Chaotic optimization algorithms, which have the features of easy implementation, short execution time and robust mechanisms of escaping from local optimum, is a promising tool for engineering applications. In this paper, a tuning method for determining the parameters of PID control for an automatic regulator voltage (AVR) system using a chaotic optimization approach based on Lozi map is proposed. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed chaotic optimization introduces chaos mapping using Lozi map chaotic sequences which increases its convergence rate and resulting precision. Simulation results are promising and show the effectiveness of the proposed approach. Numerical simulations based on proposed PID control of an AVR system for nominal system parameters and step reference voltage input demonstrate the good performance of chaotic optimization.

Adaptive full state hybrid projective synchronization of chaotic systems with the same and different order

International Nuclear Information System (INIS)

Hu Manfeng; Xu Zhenyuan; Zhang Rong; Hu Aihua

2007-01-01

This Letter further investigates the full state hybrid projective synchronization (FSHPS) of chaotic and hyper-chaotic systems with fully unknown parameters. Based on the Lyapunov stability theory, a unified adaptive controller and parameters update law can be designed for achieving the FSHPS of chaotic and/or hyper-chaotic systems with the same and different order. Especially, for two chaotic systems with different order, reduced order MFSHPS (an acronym for modified full state hybrid projective synchronization) and increased order MFSHPS are first studied in this Letter. Five groups numerical simulations are provided to verify the effectiveness of the proposed scheme. In addition, the proposed FSHPS scheme is quite robust against the effect of noise

Synchronization of uncertain chaotic systems using a single transmission channel

International Nuclear Information System (INIS)

Feng Yong; Yu Xinghuo; Sun Lixia

2008-01-01

This paper proposes a robust sliding mode observer for synchronization of uncertain chaotic systems with multi-nonlinearities. A new control strategy is proposed for the construction of the robust sliding mode observer, which can avoid the strict conditions in the design process of Walcott-Zak observer. A new method of multi-dimensional signal transmission via single transmission channel is proposed and applied to chaos synchronization of uncertain chaotic systems with multi-nonlinearities. The simulation results are presented to validate the method

Cryptanalysis of a discrete-time synchronous chaotic encryption system

International Nuclear Information System (INIS)

Arroyo, David; Alvarez, Gonzalo; Li Shujun; Li Chengqing; Nunez, Juana

2008-01-01

Recently a chaotic cryptosystem based on discrete-time synchronization has been proposed. Some weaknesses of that new encryption system are addressed and exploited in order to successfully cryptanalyze the system

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

International Nuclear Information System (INIS)

Jia Li-Xin; Dai Hao; Hui Meng

2010-01-01

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

Adaptive generalized function projective lag synchronization of different chaotic systems with fully uncertain parameters

International Nuclear Information System (INIS)

Wu Xiangjun; Lu Hongtao

2011-01-01

Highlights: → Adaptive generalized function projective lag synchronization (AGFPLS) is proposed. → Two uncertain chaos systems are lag synchronized up to a scaling function matrix. → The synchronization speed is sensitively influenced by the control gains. → The AGFPLS scheme is robust against noise perturbation. - Abstract: In this paper, a novel projective synchronization scheme called adaptive generalized function projective lag synchronization (AGFPLS) is proposed. In the AGFPLS method, the states of two different chaotic systems with fully uncertain parameters are asymptotically lag synchronized up to a desired scaling function matrix. By means of the Lyapunov stability theory, an adaptive controller with corresponding parameter update rule is designed for achieving AGFPLS between two diverse chaotic systems and estimating the unknown parameters. This technique is employed to realize AGFPLS between uncertain Lue chaotic system and uncertain Liu chaotic system, and between Chen hyperchaotic system and Lorenz hyperchaotic system with fully uncertain parameters, respectively. Furthermore, AGFPLS between two different uncertain chaotic systems can still be achieved effectively with the existence of noise perturbation. The corresponding numerical simulations are performed to demonstrate the validity and robustness of the presented synchronization method.

Analysis of transition between chaos and hyper-chaos of an improved hyper-chaotic system

International Nuclear Information System (INIS)

Qiao-Lun, Gu; Tie-Gang, Gao

2009-01-01

An improved hyper-chaotic system based on the hyper-chaos generated from Chen's system is presented, and some basic dynamical properties of the system are investigated by means of Lyapunov exponent spectrum, bifurcation diagrams and characteristic equation roots. Simulations show that the new improved system evolves into hyper-chaotic, chaotic, various quasi-periodic or periodic orbits when one parameter of the system is fixed to be a certain value while the other one is variable. Some computer simulations and bifurcation analyses are given to testify the findings. (general)

Synchronizing the noise-perturbed Lue chaotic system

International Nuclear Information System (INIS)

Zhang Yan; Chen Shihua; Zhou Hong

2009-01-01

In this paper, synchronization between unidirectionally coupled Lue chaotic systems with noise perturbation is investigated theoretically and numerically. Sufficient conditions of synchronization between these noise-perturbed systems are established by means of the so-called sliding mode control method. Some numerical simulations are also included to visualize the effectiveness and the feasibility of the developed approach.

Chaotic Boltzmann machines

Science.gov (United States)

Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki

2013-01-01

The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425

Elementary chaotic snap flows

International Nuclear Information System (INIS)

Munmuangsaen, Buncha; Srisuchinwong, Banlue

2011-01-01

Highlights: → Five new elementary chaotic snap flows and a generalization of an existing chaotic snap flow have been presented. → Three of all are conservative systems whilst three others are dissipative systems. → Four cases need only a single control parameter and a single nonlinearity. → A cubic case in a jerk representation requires only two terms and a single nonlinearity. - Abstract: Hyperjerk systems with 4th-order derivative of the form x .... =f(x ... ,x .. ,x . ,x) have been referred to as snap systems. Five new elementary chaotic snap flows and a generalization of an existing flow are presented through an extensive numerical search. Four of these flows demonstrate elegant simplicity of a single control parameter based on a single nonlinearity of a quadratic, a piecewise-linear or an exponential type. Two others demonstrate elegant simplicity of all unity-in-magnitude parameters based on either a single cubic nonlinearity or three cubic nonlinearities. The chaotic snap flow with a single cubic nonlinearity requires only two terms and can be transformed to its equivalent dynamical form of only five terms which have a single nonlinearity. An advantage is that such a chaotic flow offers only five terms even though the (four) dimension is high. Three of the chaotic snap flows are characterized as conservative systems whilst three others are dissipative systems. Basic dynamical properties are described.

Quantum-chaotic cryptography

Science.gov (United States)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Samuel Pepys and corruption

OpenAIRE

Knights, Mark

2014-01-01

Picking up a theme that runs through David Hayton's work, this article examines corruption in the later Stuart period through a case study of Samuel Pepys. The latter's diary can be read alongside the public record of parliamentary inquiries and vilification in the press, allowing us a rare opportunity to study corruption simultaneously through the eyes of a perpetrator and his critics. Pepys reveals ambiguities in how corruption was defined and defended. At the same time as he criticized cor...

Synchronization of Harb-Zohdy Chaotic System via Back-Stepping Design

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M. R. Shamsyeh Zahedi∗

2015-12-01

Full Text Available This paper is concerned with the problem of synchronization of the Harb-Zohdy chaotic system using the back-stepping. Based on the stability theory, the control for the synchronization of chaotic systems Harb-Zohdy is considered without unknown parameters. Next, an adaptive back-stepping control law is derived to generate an error signal between the drive and response systems Harb-Zohdy with an uncertain parameter asymptotically synchronized. Finally, this method is extended to synchronize the system with two unknown parameters. Note that the method presented here needs only one controller to realize the synchronization. Numerical simulations indicate the effectiveness of the proposed chaos synchronization scheme

Dispersion compensation in an open-loop all-optical chaotic communication system

International Nuclear Information System (INIS)

Liu Hui-Jie; Feng Jiu-Chao; Ren Bin

2012-01-01

The optical chaotic communication system using open-loop fiber transmission is studied under strong injection conditions. The optical chaotic communication system with open-loop configuration is studied using fiber transmission under strong injection conditions. The performances of fiber links composed of two types of fiber segments in different dispersion compensation maps are compared by testing the quality of the recovered message with different bit rates and encrypted by chaotic modulation (CM) or chaotic shift keying (CSK). The result indicates that the performance of the pre-compensation map is always worst. Two types of symmetrical maps are identical whatever the encryption method and bit-rate of message are. For the transmitting and the recovering of message of lower bit rate (1 Gb/s), the post-compensation map is the best scheme. However, for the message of higher bit rate (2.5 Gb/s), the parameters in communication system need to be modified properly in order to adapt to the high-speed application. Meanwhile, two types of symmetrical maps are the best scheme. In addition, the CM method is superior to the CSK method for high-speed applications. It is in accordance with the result in a back-to-back configuration system. (general)

Design of output feedback controller for a unified chaotic system

International Nuclear Information System (INIS)

Li Wenlin; Chen Xiuqin; Shen Zhiping

2008-01-01

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method

Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems

International Nuclear Information System (INIS)

Chen, J.-H.; Chen, H.-K.; Lin, Y.-K.

2009-01-01

This study demonstrates that synchronization and anti-synchronization can coexist in Chen-Lee chaotic systems by direct linear coupling. Based on Lyapunov's direct method, a linear controller was designed to assure that two different types of synchronization can simultaneously be achieved. Further, the hybrid projective synchronization of Chen-Lee chaotic systems was studied using a nonlinear control scheme. The nonlinear controller was designed according to the Lyapunov stability theory to guarantee the hybrid projective synchronization, including synchronization, anti-synchronization, and projective synchronization. Finally, numerical examples are presented in order to illustrate the proposed synchronization approach.

Adaptive variable structure control for uncertain chaotic systems containing dead-zone nonlinearity

International Nuclear Information System (INIS)

Yan, J.-J.; Shyu, K.-K.; Lin, J.-S.

2005-01-01

This paper addresses a practical tracking problem for a class of uncertain chaotic systems with dead-zone nonlinearity in the input function. Based on the Lyapunov stability theorem and Barbalat lemma, an adaptive variable structure controller (AVSC) is proposed to ensure the occurrence of the sliding mode even though the control input contains a dead-zone. Also it is worthy of note that the proposed AVSC involves no information of the upper bound of uncertainty. Thus, the limitation of knowing the bound of uncertainty in advance is certainly released. Furthermore, in the sliding mode, the investigated uncertain chaotic system remains insensitive to the uncertainty, and behaves like a linear system. Finally, a well-known Duffing-Holmes chaotic system is used to demonstrate the feasibility of the proposed AVSC

Cryptanalysis of a chaotic secure communication system

International Nuclear Information System (INIS)

Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G.

2003-01-01

Recently a chaotic encryption system has been proposed by P. Garcia et al. It represents an improvement over an algorithm previously presented by some of the same authors. In this Letter, several weaknesses of the new cryptosystem are pointed out and four successful cryptanalytic attacks are described

A controllability approach to the control of a class of chaotic systems

International Nuclear Information System (INIS)

Bowong, Samuel; Moukam Kakmeni, F.M.; Tchawoua, Clement; Abdus Salam International Centre for Theoretical Physics, Trieste

2003-10-01

In this paper the exponential control problem for a class of chaotic systems with affine dependence on the control is addressed and solved by the controllability approach. It is shown that the controllability approach in conjunction with Lyapunov Direct Method yields a promising way of controlling chaotic dynamics. The proposed strategy is an input-output control scheme which comprises a state estimator and an exponential linearizing feedback. The proposed output feedback controller allows chaos suppression and can be applied to a large class of chaotic systems. Explicit expression of the control time is given. Computer simulations confirm the feasibility of the proposed approach. (author)

A unified approach for impulsive lag synchronization of chaotic systems with time delay

International Nuclear Information System (INIS)

Li Chuandong; Liao Xiaofeng; Zhang Rong

2005-01-01

In this paper, we propose a unified approach for impulsive lag-synchronization of a class of chaotic systems with time delay by employing the stability theory of impulsive delayed differential equations. Three well-known delayed chaotic systems are presented to illustrate our results. Also, the estimates of the stable regions for these systems are given, respectively

High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving

Science.gov (United States)

Qiu, Junchao; Zhang, Lin; Li, Diyang; Liu, Xingcheng

2016-06-01

Chaotic sequences can be applied to realize multiple user access and improve the system security for a visible light communication (VLC) system. However, since the map patterns of chaotic sequences are usually well known, eavesdroppers can possibly derive the key parameters of chaotic sequences and subsequently retrieve the information. We design an advanced encryption standard (AES) interleaving aided multiple user access scheme to enhance the security of a chaotic code division multiple access-based visible light communication (C-CDMA-VLC) system. We propose to spread the information with chaotic sequences, and then the spread information is interleaved by an AES algorithm and transmitted over VLC channels. Since the computation complexity of performing inverse operations to deinterleave the information is high, the eavesdroppers in a high speed VLC system cannot retrieve the information in real time; thus, the system security will be enhanced. Moreover, we build a mathematical model for the AES-aided VLC system and derive the theoretical information leakage to analyze the system security. The simulations are performed over VLC channels, and the results demonstrate the effectiveness and high security of our presented AES interleaving aided chaotic CDMA-VLC system.

Control uncertain Genesio-Tesi chaotic system: Adaptive sliding mode approach

International Nuclear Information System (INIS)

Dadras, Sara; Momeni, Hamid Reza

2009-01-01

An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio-Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio-Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.

Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity

International Nuclear Information System (INIS)

Sun, Y.-J.

2009-01-01

In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.

Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters

International Nuclear Information System (INIS)

Chen Yong; Li Xin

2009-01-01

The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme. (general)

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

International Nuclear Information System (INIS)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.

2016-01-01

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

Active synchronization between two different chaotic dynamical system

International Nuclear Information System (INIS)

Maheri, M.; Arifin, N. Md; Ismail, F.

2015-01-01

In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes

Active synchronization between two different chaotic dynamical system

Energy Technology Data Exchange (ETDEWEB)

Maheri, M. [Institute for Mathematical Research, 43400 UPM, Serdang, Selengor (Malaysia); Arifin, N. Md; Ismail, F. [Department of Mathematics, 43400 UPM, Serdang, Selengor (Malaysia)

2015-05-15

In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.

The control of an optical hyper-chaotic system

International Nuclear Information System (INIS)

Jiang Shumin; Tian Lixin; Wang Xuedi

2007-01-01

This paper discusses the problem of hyper-chaos control of an optical system. Based on Lyapunov stability theory, a non-autonomous feedback controller is designed. The proposed controller ensures that the hyper-chaotic system will be asymptotically stable. Numerical simulation of the original and the controlled system is provided to show the effectiveness of our method

Sliding mode control for uncertain unified chaotic systems with input nonlinearity

International Nuclear Information System (INIS)

Chiang, T.-Y.; Hung, M.-L.; Yan, J.-J.; Yang, Y.-S.; Chang, J.-F.

2007-01-01

This paper investigates the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Using the sliding mode control technique, a robust control law is established which stabilizes the uncertain unified chaotic systems even when the nonlinearity in the actuators is present. A novel adaptive switching surface is introduced to simplify the task of assigning the stability of the closed-loop system in the sliding mode motion. An illustrative example is given to demonstrate the effectiveness of the proposed sliding mode control design

Chaotic incommensurate fractional order Rössler system: active control and synchronization

Directory of Open Access Journals (Sweden)

Baleanu Dumitru

2011-01-01

Full Text Available Abstract In this article, we present an active control methodology for controlling the chaotic behavior of a fractional order version of Rössler system. The main feature of the designed controller is its simplicity for practical implementation. Although in controlling such complex system several inputs are used in general to actuate the states, in the proposed design, all states of the system are controlled via one input. Active synchronization of two chaotic fractional order Rössler systems is also investigated via a feedback linearization method. In both control and synchronization, numerical simulations show the efficiency of the proposed methods.

Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map

International Nuclear Information System (INIS)

Bonakdar, Mohammad; Samadi, Mostafa; Salarieh, Hassan; Alasty, Aria

2008-01-01

In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed

Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map

Energy Technology Data Exchange (ETDEWEB)

Bonakdar, Mohammad; Samadi, Mostafa [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of); Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)

2008-05-15

In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed.

On the synchronization of identical and non-identical 4-D chaotic systems using arrow form matrix

International Nuclear Information System (INIS)

Hammami, S.; Ben Saad, K.; Benrejeb, M.

2009-01-01

Using the Borne and Gentina practical criterion associated with the Benrejeb canonical arrow form matrix, to derive the stability property of dynamic complex systems, a new strategy of control is formulated for chaos synchronization of two identical Lorenz Stenflo systems and two new four-dimensional chaotic systems, namely the Qi chaotic systems. The designed controller ensures that the state variables of both controlled chaotic slave Lorenz Stenflo and Qi systems globally synchronizes with the state variables of the master systems, respectively. It is also shown that Qi system globally synchronizes with Lorenz Stenflo system under the afforded generalized strategy of control. Numerical simulations are carried out to assess the performance of the proposed contributions in the important field of chaotic synchronization.

Samuel Taylor Coleridge’s

Directory of Open Access Journals (Sweden)

Aslı TEKİNAY

2000-01-01

Full Text Available There is a dark strain which can be traced in the poetry of all the major nineteenth century English romantic poets: a scepticism about the ultimate purpose of man's life, a sense of having lost a metaphysical certainty and faith in the presence of a benevolent power who maintains harmony and order in the universe. Samuel Taylor Coleridge is one of them. In "The Rime of the Ancient Mariner" and "Christabel", he reveals a nightmarish vision of the universe where moral order seems to be replaced by a cosmic "hap".

A novel hybrid color image encryption algorithm using two complex chaotic systems

Science.gov (United States)

Wang, Leyuan; Song, Hongjun; Liu, Ping

2016-02-01

Based on complex Chen and complex Lorenz systems, a novel color image encryption algorithm is proposed. The larger chaotic ranges and more complex behaviors of complex chaotic systems, which compared with real chaotic systems could additionally enhance the security and enlarge key space of color image encryption. The encryption algorithm is comprised of three step processes. In the permutation process, the pixels of plain image are scrambled via two-dimensional and one-dimensional permutation processes among RGB channels individually. In the diffusion process, the exclusive-or (XOR for short) operation is employed to conceal pixels information. Finally, the mixing RGB channels are used to achieve a multilevel encryption. The security analysis and experimental simulations demonstrate that the proposed algorithm is large enough to resist the brute-force attack and has excellent encryption performance.

Investigation of a Unified Chaotic System and Its Synchronization by Simulations

International Nuclear Information System (INIS)

Qing-Chu, Wu; Xin-Chu, Fu; Small, Michael

2010-01-01

We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent. (general)

Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication

Directory of Open Access Journals (Sweden)

Shouquan Pang

2016-01-01

Full Text Available Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.

Synchronization of chaotic systems involving fractional operators of Liouville-Caputo type with variable-order

Science.gov (United States)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.

2017-12-01

In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

Fully Digital Chaotic Differential Equation-based Systems And Methods

KAUST Repository

Radwan, Ahmed Gomaa Ahmed; Zidan, Mohammed A.; Salama, Khaled N.

2012-01-01

Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.

Fully Digital Chaotic Differential Equation-based Systems And Methods

KAUST Repository

Radwan, Ahmed Gomaa Ahmed

2012-09-06

Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.

Applications of modularized circuit designs in a new hyper-chaotic system circuit implementation

Science.gov (United States)

Wang, Rui; Sun, Hui; Wang, Jie-Zhi; Wang, Lu; Wang, Yan-Chao

2015-02-01

Modularized circuit designs for chaotic systems are introduced in this paper. Especially, a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation. In this paper, the detailed design procedures are described. Multisim simulations and physical experiments are conducted, and the simulation results are compared with Matlab simulation results for different system parameter pairs. These results are consistent with each other and they verify the existence of the hyper-chaotic attractor for this new hyper-chaotic system. Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61403395), the Natural Science Foundation of Tianjin, China (Grant No. 13JCYBJC39000), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China, the Fund from the Tianjin Key Laboratory of Civil Aircraft Airworthiness and Maintenance in Civil Aviation of China (Grant No. 104003020106), the National Basic Research Program of China (Grant No. 2014CB744904), and the Fund for the Scholars of Civil Aviation University of China (Grant No. 2012QD21x).

Adaptive Control of the Chaotic System via Singular System Approach

Directory of Open Access Journals (Sweden)

Yudong Li

2014-01-01

Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.

Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation

Science.gov (United States)

Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin

2017-12-01

Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.

A new chaotic secure communication scheme

International Nuclear Information System (INIS)

Hua Changchun; Yang Bo; Ouyang Gaoxiang; Guan Xinping

2005-01-01

A new chaotic secure communication scheme is constructed. Unified chaotic system is used to encrypt the emitted signal. Different from the existing chaotic secure communication methods, the useful information is embodied in the parameter of chaotic systems in this Letter. The receiver is designed which can succeed in recovering the former signal. Finally computer simulations are done to verify the proposed methods, and the results show that the obtained theoretic results are feasible and efficient

Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control

Directory of Open Access Journals (Sweden)

Chunyan Han

2015-01-01

Full Text Available Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise linear chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems by switching control. Finally, another multipiecewise linear chaotic system that also satisfies the Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multipiecewise linear system. Some basic dynamical characteristics, including divergence, Lyapunov exponents, and bifurcation diagrams of the constructed systems, are analyzed. Meanwhile, computer simulation and circuit design are used for the proposed chaotic systems, and they are demonstrated to be effective for the method of chaos anticontrol.

Gross-Pitaevski map as a chaotic dynamical system.

Science.gov (United States)

Guarneri, Italo

2017-03-01

The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.

Samuel Thomas Soemmerring (1755-1830): The Naming of Cranial Nerves.

Science.gov (United States)

Pearce, John M S

2017-01-01

Samuel Thomas Soemmerring was a Prussian polymathic doctor with remarkable achievements in anatomy, draftsmanship and inventions. His naming of 12 pairs of cranial nerves in his graduation thesis is of particular importance. He also gave original descriptions of the macula, sensory pathways and of the substantia nigra. His non-medical contributions were diverse and included criticism of the guillotine, invention of a telegraphic system, and discoveries in palaeontology. © 2017 S. Karger AG, Basel.

Feedback control and adaptive control of the energy resource chaotic system

International Nuclear Information System (INIS)

Sun Mei; Tian Lixin; Jiang Shumin; Xu Jun

2007-01-01

In this paper, the problem of control for the energy resource chaotic system is considered. Two different method of control, feedback control (include linear feedback control, non-autonomous feedback control) and adaptive control methods are used to suppress chaos to unstable equilibrium or unstable periodic orbits. The Routh-Hurwitz criteria and Lyapunov direct method are used to study the conditions of the asymptotic stability of the steady states of the controlled system. The designed adaptive controller is robust with respect to certain class of disturbances in the energy resource chaotic system. Numerical simulations are presented to show these results

An improved harmony search algorithm for synchronization of discrete-time chaotic systems

International Nuclear Information System (INIS)

Santos Coelho, Leandro dos; Andrade Bernert, Diego Luis de

2009-01-01

The harmony search (HS) algorithm is a recently developed meta-heuristic algorithm, and has been very successful in a wide variety of optimization problems. HS was conceptualized using an analogy with music improvisation process where music players improvise the pitches of their instruments to obtain better harmony. The HS algorithm does not require initial values and uses a random search instead of a gradient search, so derivative information is unnecessary. Furthermore, the HS algorithm is simple in concept, few in parameters, easy in implementation, imposes fewer mathematical requirements, and does not require initial value settings of the decision variables. In recent years, the investigation of synchronization and control problem for discrete chaotic systems has attracted much attention, and many possible applications. The tuning of a proportional-integral-derivative (PID) controller based on an improved HS (IHS) algorithm for synchronization of two identical discrete chaotic systems subject the different initial conditions is investigated in this paper. Simulation results of the IHS to determine the PID parameters to synchronization of two Henon chaotic systems are compared with other HS approaches including classical HS and global-best HS. Numerical results reveal that the proposed IHS method is a powerful search and controller design optimization tool for synchronization of chaotic systems.

Multiscality in the Dynamics of Coupled Chaotic Systems

DEFF Research Database (Denmark)

Pavlov, A.N.; Sosnovtseva, Olga; Ziganshin, A.R.

2002-01-01

We investigate the scaling features of complex motions in systems of two coupled chaotic oscillators by means of the wavelet-transform modulus maxima method and the detrended fluctuation analysis. We show that the transition from asynchronous to synchronous dynamics typically reduces the degree...

Synchronization of spatiotemporal chaotic systems by feedback control

International Nuclear Information System (INIS)

Lai, Y.; Grebogi, C.

1994-01-01

We demonstrate that two identical spatiotemporal chaotic systems can be synchronized by (1) linking one or a few of their dynamical variables, and (2) applying a small feedback control to one of the systems. Numerical examples using the diffusively coupled logistic map lattice are given. The effect of noise and the limitation of the technique are discussed

From determinism and probability to chaos: chaotic evolution towards philosophy and methodology of chaotic optimization.

Science.gov (United States)

Pei, Yan

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

Science.gov (United States)

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

Directory of Open Access Journals (Sweden)

Yan Pei

2015-01-01

Full Text Available We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC algorithm, interactive chaotic evolution (ICE that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

Visibility graphlet approach to chaotic time series

Energy Technology Data Exchange (ETDEWEB)

Mutua, Stephen [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega (Kenya); Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn; Yang, Huijie, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)

2016-05-15

Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.

Exponential networked synchronization of master-slave chaotic systems with time-varying communication topologies

International Nuclear Information System (INIS)

Yang Dong-Sheng; Liu Zhen-Wei; Liu Zhao-Bing; Zhao Yan

2012-01-01

The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time-varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method. (general)

Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

Directory of Open Access Journals (Sweden)

Jianeng Tang

2014-01-01

Full Text Available Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.

Synchronizing strict-feedback and general strict-feedback chaotic systems via a single controller

International Nuclear Information System (INIS)

Chen Shihua; Wang Feng; Wang Changping

2004-01-01

We present a systematic design procedure to synchronize a class of chaotic systems in a so-called strict-feedback form based on back-stepping procedure. This approach needs only a single controller to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, we point out that the method does not work for general strict-feedback chaotic systems, for instance, Lorenz system. Therefore, we propose three kinds of synchronization schemes for Lorenz system using the Lyapunov function method. All the three schemes avoid including divergence factor as in Ref. [Chaos, Solitons and Fractals 16 (2003) 37]. Especially in the last two schemes, we need only one state variable in controller, which has important significance in chaos synchronization used for communication purposes. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods

Identification of chaotic systems with hidden variables (modified Bock's algorithm)

International Nuclear Information System (INIS)

Bezruchko, Boris P.; Smirnov, Dmitry A.; Sysoev, Ilya V.

2006-01-01

We address the problem of estimating parameters of chaotic dynamical systems from a time series in a situation when some of state variables are not observed and/or the data are very noisy. Using specially developed quantitative criteria, we compare performance of the original multiple shooting approach (Bock's algorithm) and its modified version. The latter is shown to be significantly superior for long chaotic time series. In particular, it allows to obtain accurate estimates for much worse starting guesses for the estimated parameters

Finite-time synchronization of Lorenz chaotic systems: theory and circuits

International Nuclear Information System (INIS)

Louodop, Patrick; Fotsin, Hilaire; Kountchou, Michaux; Bowong, Samuel

2013-01-01

This paper addresses the problem of finite-time master–slave synchronization of Lorenz chaotic systems from a control theoretic point of view. We propose a family of feedback couplings which accomplish the synchronization of Lorenz chaotic systems based on Lyapunov stability theory. These feedback couplings are based on non-periodic functions. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at established time. An advantage is that some of the proposed feedback couplings are simple and easy to implement. Both mathematical investigations and numerical simulations followed by a Pspice experiment are presented to show the feasibility of the proposed method. (paper)

On dynamics analysis of a new chaotic attractor

International Nuclear Information System (INIS)

Zhou Wuneng; Xu Yuhua; Lu Hongqian; Pan Lin

2008-01-01

In this Letter, a new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincare mapping, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed in this Letter is a new chaotic system and deserves a further detailed investigation

Synchronization in node of complex networks consist of complex chaotic system

Energy Technology Data Exchange (ETDEWEB)

Wei, Qiang, E-mail: qiangweibeihua@163.com [Beihua University computer and technology College, BeiHua University, Jilin, 132021, Jilin (China); Digital Images Processing Institute of Beihua University, BeiHua University, Jilin, 132011, Jilin (China); Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024 (China); Xie, Cheng-jun [Beihua University computer and technology College, BeiHua University, Jilin, 132021, Jilin (China); Digital Images Processing Institute of Beihua University, BeiHua University, Jilin, 132011, Jilin (China); Liu, Hong-jun [School of Information Engineering, Weifang Vocational College, Weifang, 261041 (China); Li, Yan-hui [The Library, Weifang Vocational College, Weifang, 261041 (China)

2014-07-15

A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.

Chaos control of Chen chaotic dynamical system

International Nuclear Information System (INIS)

Yassen, M.T.

2003-01-01

This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results

Parameter estimation for chaotic systems with a Drift Particle Swarm Optimization method

International Nuclear Information System (INIS)

Sun Jun; Zhao Ji; Wu Xiaojun; Fang Wei; Cai Yujie; Xu Wenbo

2010-01-01

Inspired by the motion of electrons in metal conductors in an electric field, we propose a variant of Particle Swarm Optimization (PSO), called Drift Particle Swarm Optimization (DPSO) algorithm, and apply it in estimating the unknown parameters of chaotic dynamic systems. The principle and procedure of DPSO are presented, and the algorithm is used to identify Lorenz system and Chen system. The experiment results show that for the given parameter configurations, DPSO can identify the parameters of the systems accurately and effectively, and it may be a promising tool for chaotic system identification as well as other numerical optimization problems in physics.

A simple chaotic delay differential equation

International Nuclear Information System (INIS)

Sprott, J.C.

2007-01-01

The simplest chaotic delay differential equation with a sinusoidal nonlinearity is described, including the route to chaos, Lyapunov exponent spectrum, and chaotic diffusion. It is prototypical of many other high-dimensional chaotic systems

Modeling of Coupled Chaotic Oscillators

International Nuclear Information System (INIS)

Lai, Y.; Grebogi, C.

1999-01-01

Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations. copyright 1999 The American Physical Society

A chaotic system with a single unstable node

Energy Technology Data Exchange (ETDEWEB)

Sprott, J.C. [Department of Physics, University of Wisconsin, Madison, WI 53706 (United States); Jafari, Sajad, E-mail: sajadjafari@aut.ac.ir [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Pham, Viet-Thanh [School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi (Viet Nam); Hosseini, Zahra Sadat [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of)

2015-09-25

This paper describes an unusual example of a three-dimensional dissipative chaotic flow with quadratic nonlinearities in which the only equilibrium is an unstable node. The region of parameter space with bounded solutions is relatively small as is the basin of attraction, which accounts for the difficulty of its discovery. Furthermore, for some values of the parameters, the system has an attracting torus, which is uncommon in three-dimensional systems, and this torus can coexist with a strange attractor or with a limit cycle. The limit cycle and strange attractor exhibit symmetry breaking and attractor merging. All the attractors appear to be hidden in that they cannot be found by starting with initial conditions in the vicinity of the equilibrium, and thus they represent a new type of hidden attractor with important and potentially problematic engineering consequences. - Highlights: • An unusual example of a three-dimensional dissipative chaotic flow is introduced. • In this system the only equilibrium is an unstable node. • For some values of the parameters, the system has an attracting torus. • This torus can coexist with a strange attractor or with a limit cycle. • These properties are uncommon in three-dimensional systems.

Universality for the parameter-mismatching effect on weak synchronization in coupled chaotic systems

International Nuclear Information System (INIS)

Lim, Woochang; Kim, Sang-Yoon

2004-01-01

To examine the universality for the parameter-mismatching effect on weak chaotic synchronization, we study coupled multidimensional invertible systems such as the coupled Henon maps and coupled pendula. By generalizing the method proposed in coupled one-dimensional (1D) noninvertible maps, we introduce the parameter sensitivity exponent δ to measure the degree of the parameter sensitivity of a weakly stable synchronous chaotic attractor. In terms of the parameter sensitivity exponents, we characterize the effect of the parameter mismatch on the intermittent bursting and the basin riddling occurring in the regime of weak synchronization. It is thus found that the scaling exponent μ for the average characteristic time (i.e., the average interburst time and the average chaotic transient lifetime) for both the bubbling and riddling cases is given by the reciprocal of the parameter sensitivity exponent, as in the simple system of coupled 1D maps. Hence, the reciprocal relation (i.e., μ = 1/δ) seems to be 'universal', in the sense that it holds in typical coupled chaotic systems of different nature

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

Science.gov (United States)

Mallory, Kristina; van Gorder, Robert A.

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified Lue chaotic system

International Nuclear Information System (INIS)

Xu Yuhua; Zhou Wuneng; Fang Jianan

2009-01-01

This paper introduces a modified Lue chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lue chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods.

Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified Lue chaotic system

Energy Technology Data Exchange (ETDEWEB)

Xu Yuhua [College of Information Science and Technology, Donghua University, Shanghai 201620 (China) and Department of Maths, Yunyang Teacher' s College, Hubei 442000 (China)], E-mail: yuhuaxu2004@163.com; Zhou Wuneng [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)], E-mail: wnzhou@163.com; Fang Jianan [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)

2009-11-15

This paper introduces a modified Lue chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lue chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods.

Stochastic Resonance in a System of Coupled Chaotic Oscillators

International Nuclear Information System (INIS)

Krawiecki, A.

1999-01-01

Noise-free stochastic resonance is investigated numerically in a system of two coupled chaotic Roessler oscillators. Periodic signal is applied either additively or multiplicatively to the coupling term. When the coupling constant is varied the oscillators lose synchronization via attractor bubbling or on-off intermittency. Properly chosen signals are analyzed which reflect the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. Maximum of the signal-to-noise ratio as a function of the coupling constant is observed. Dependence of the signal-to-noise ratio on the frequency of the periodic signal and parameter mismatch between the oscillators is investigated. Possible applications of stochastic resonance in the recovery of signals in secure communication systems based on chaotic synchronization are briefly discussed. (author)

In Memoriam: Arthur Samuel: Pioneer in Machine Learning

OpenAIRE

McCarthy, John; Feigenbaum, Edward A.

1990-01-01

Arthur Samuel (1901-1990) was a pioneer of artificial intelligence research. From 1949 through the late 1960s, he did the best work in making computers learn from their expe-rience. His vehicle for this work was the game of checkers.

Reconfigurable chaotic logic gates based on novel chaotic circuit

International Nuclear Information System (INIS)

Behnia, S.; Pazhotan, Z.; Ezzati, N.; Akhshani, A.

2014-01-01

Highlights: • A novel method for implementing logic gates based on chaotic maps is introduced. • The logic gates can be implemented without any changes in the threshold voltage. • The chaos-based logic gates may serve as basic components of future computing devices. - Abstract: The logical operations are one of the key issues in today’s computer architecture. Nowadays, there is a great interest in developing alternative ways to get the logic operations by chaos computing. In this paper, a novel implementation method of reconfigurable logic gates based on one-parameter families of chaotic maps is introduced. The special behavior of these chaotic maps can be utilized to provide same threshold voltage for all logic gates. However, there is a wide interval for choosing a control parameter for all reconfigurable logic gates. Furthermore, an experimental implementation of this nonlinear system is presented to demonstrate the robustness of computing capability of chaotic circuits

Mechanical analysis of Chen chaotic system

International Nuclear Information System (INIS)

Liang, Xiyin; Qi, Guoyuan

2017-01-01

The Chen chaotic system is transformed into Kolmogorov type system, which is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. By the combinations of different torques, five cases are studied to discover key factors of chaos generation and the physical meaning. The conversion among Hamiltonian energy, kinetic energy and potential energy is investigated in these five cases. The relationship between the energies and the parameters is studied. It concludes that the combination of these four types of torques is necessary conditions to produce chaos, and any combination of three types of torques cannot produce chaos in Chen system.

Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control

Energy Technology Data Exchange (ETDEWEB)

Layeghi, Hamed [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: layeghi@mech.sharif.edu; Arjmand, Mehdi Tabe [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: arjmand@mech.sharif.edu; Salarieh, Hassan [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu

2008-08-15

In this paper by using a combination of fuzzy identification and the sliding mode control a fuzzy adaptive sliding mode scheme is designed to stabilize the unstable periodic orbits of chaotic systems. The chaotic system is assumed to have an affine form x{sup (n)} = f(X) + g(X)u where f and g are unknown functions. Using only the input-output data obtained from the underlying dynamical system, two fuzzy systems are constructed for identification of f and g. Two distinct methods are utilized for fuzzy modeling, the least squares and the gradient descent techniques. Based on the estimated fuzzy models, an adaptive controller, which works through the sliding mode control, is designed to make the system track the desired unstable periodic orbits. The stability analysis of the overall closed loop system is presented in the paper and the effectiveness of the proposed adaptive scheme is numerically investigated. As a case of study, modified Duffing system is selected for applying the proposed method to stabilize its 2{pi} and 4{pi} periodic orbits. Simulation results show the high performance of the method for stabilizing the unstable periodic orbits of unknown chaotic systems.

Projective-anticipating, projective and projective-lag synchronization of chaotic systems with time-varying delays

International Nuclear Information System (INIS)

Feng Cunfang; Guan Wei; Wang Yinghai

2013-01-01

We investigate different types of projective (projective-anticipating, projective and projective-lag) synchronization in unidirectionally nonlinearly coupled time-delayed chaotic systems with variable time delays. Based on the Krasovskii–Lyapunov approach, we find both the existence and sufficient stability conditions, using a general class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. Our method has the advantage that it requires only one nonlinearly coupled term to achieve different types of projective synchronization in time-delayed chaotic systems with variable time delays. Compared with other existing works, our result provides an easy way to achieve projective-anticipating, projective and projective-lag synchronization. Numerical simulations of the Ikeda system are given to demonstrate the validity of the proposed method. (paper)

Samuel Barnsley Pessoa e os determinantes sociais das endemias rurais

Directory of Open Access Journals (Sweden)

Gilberto Hochman

2015-02-01

Full Text Available O artigo analisa os principais aspectos da trajetória, das ideias e da atuação acadêmica e política de Samuel Barnsley Pessoa (1898-1976. Indica que a atuação de Samuel Pessoa deve ser compreendida também a partir da sua militância comunista e ressalta que uma das contribuições originais de seus trabalhos foi o estabelecimento da relação entre estrutura agrária e endemias rurais, entre latifúndio e doença e a adesão a um projeto de transformação da sociedade brasileira.

Chaotic scattering and quantum dynamics

International Nuclear Information System (INIS)

Doron, Eyal.

1992-11-01

The main concern of this thesis is the application of the semiclassical approximation to quantum chaotic scattering systems. We deal with two separate, although interconnected, subjects. The first subject dealt with is the semiclassical characterization of the fluctuations of the S matrix. A particular important parameter is the magnetic field B, and we show how the correlation length and line shape of S matrix elements under a change of B may be derived. An effect which is present in many physical wave systems is absorption of energy flux. We show how absorption affects both the reflectivity and the scattering phase and time delay of a scattering system. In the second part of the thesis, we show how the formalism and results obtained from chaotic scattering can be applied to the investigation of closed chaotic systems, and in particular to chaotic billiards. The semiclassical expansion for billiards is presented. In the last part of the thesis we deal with the statistics of S matrices of chaotic scattering systems. The main message of this work is that scattering matrix, and its classical counterpart the Poincare Scattering Map can be used to yield a powerful formulation of the quantum mechanical dynamics of bounded systems. (author)

Comparison between different synchronization methods of identical chaotic systems

International Nuclear Information System (INIS)

Haeri, Mohammad; Khademian, Behzad

2006-01-01

This paper studies and compares three nonadaptive (bidirectional, unidirectional, and sliding mode) and two adaptive (active control and backstepping) synchronization methods on the synchronizing of four pairs of identical chaotic systems (Chua's circuit, Roessler system, Lorenz system, and Lue system). Results from computer simulations are presented in order to illustrate the effectiveness of the methods and to compare them based on different criteria

Chaos control in delayed chaotic systems via sliding mode based delayed feedback

Energy Technology Data Exchange (ETDEWEB)

Vasegh, Nastaran [Faculty of Electrical Engineering, K.N. Toosi University of Technology, Seyed Khandan Bridge, Shariati St. 16314, P.O. Box 16315-1355, Tehran (Iran, Islamic Republic of)], E-mail: vasegh@eetd.kntu.ac.ir; Sedigh, Ali Khaki [Faculty of Electrical Engineering, K.N. Toosi University of Technology, Seyed Khandan Bridge, Shariati St. 16314, P.O. Box 16315-1355, Tehran (Iran, Islamic Republic of)

2009-04-15

This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey-Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

Chaos control in delayed chaotic systems via sliding mode based delayed feedback

International Nuclear Information System (INIS)

Vasegh, Nastaran; Sedigh, Ali Khaki

2009-01-01

This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey-Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

Nonlinear Time-Reversal in a Wave Chaotic System

Science.gov (United States)

Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven

2012-02-01

Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)

Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

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Y. Saiki

2007-09-01

Full Text Available An infinite number of unstable periodic orbits (UPOs are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

Adaptive Synchronization of Chaotic Systems considering Performance Parameters of Operational Amplifiers

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Sergio Ruíz-Hernández

2015-01-01

Full Text Available This paper addresses an adaptive control approach for synchronizing two chaotic oscillators with saturated nonlinear function series as nonlinear functions. Mathematical models to characterize the behavior of the transmitter and receiver circuit were derived, including in the latter the adaptive control and taking into account, for both chaotic oscillators, the most influential performance parameters associated with operational amplifiers. Asymptotic stability of the full synchronization system is studied by using Lyapunov direct method. Theoretical derivations and related results are experimentally validated through implementations from commercially available devices. Finally, the full synchronization system can easily be reproducible at a low cost.

Analysis of the time structure of synchronization in multidimensional chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)

2015-05-15

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.

Analysis of the time structure of synchronization in multidimensional chaotic systems

International Nuclear Information System (INIS)

Makarenko, A. V.

2015-01-01

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete

Targeting engineering synchronization in chaotic systems

Science.gov (United States)

Bhowmick, Sourav K.; Ghosh, Dibakar

2016-07-01

A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in detail. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.

New Chaotic Dynamical System with a Conic-Shaped Equilibrium Located on the Plane Structure

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Jiri Petrzela

2017-09-01

Full Text Available This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.

Extreme multistability analysis of memristor-based chaotic system and its application in image decryption

Directory of Open Access Journals (Sweden)

Chuang Li

2017-12-01

Full Text Available An active charge-controlled memristive Chua’s circuit is implemented, and its basic properties are analyzed. Firstly, with the system trajectory starting from an equilibrium point, the dynamic behavior of multiple coexisting attractors depending on the memristor initial value and the system parameter is studied, which shows the coexisting behaviors of point, period, chaos, and quasic-period. Secondly, with the system motion starting from a non-equilibrium point, the dynamics of extreme multistability in a wide initial value domain are easily conformed by new analytical methods. Furthermore, the simulation results indicate that some strange chaotic attractors like multi-wing type and multi-scroll type are observed when the observed signals are extended from voltage and current to power and energy, respectively. Specially, when different initial conditions are taken, the coexisting strange chaotic attractors between the power and energy signals are exhibited. Finally, the chaotic sequences of the new system are used for encrypting color image to protect image information security. The encryption performance is analyzed by statistic histogram, correlation, key spaces and key sensitivity. Simulation results show that the new memristive chaotic system has high security in color image encryption.

Extreme multistability analysis of memristor-based chaotic system and its application in image decryption

Science.gov (United States)

Li, Chuang; Min, Fuhong; Jin, Qiusen; Ma, Hanyuan

2017-12-01

An active charge-controlled memristive Chua's circuit is implemented, and its basic properties are analyzed. Firstly, with the system trajectory starting from an equilibrium point, the dynamic behavior of multiple coexisting attractors depending on the memristor initial value and the system parameter is studied, which shows the coexisting behaviors of point, period, chaos, and quasic-period. Secondly, with the system motion starting from a non-equilibrium point, the dynamics of extreme multistability in a wide initial value domain are easily conformed by new analytical methods. Furthermore, the simulation results indicate that some strange chaotic attractors like multi-wing type and multi-scroll type are observed when the observed signals are extended from voltage and current to power and energy, respectively. Specially, when different initial conditions are taken, the coexisting strange chaotic attractors between the power and energy signals are exhibited. Finally, the chaotic sequences of the new system are used for encrypting color image to protect image information security. The encryption performance is analyzed by statistic histogram, correlation, key spaces and key sensitivity. Simulation results show that the new memristive chaotic system has high security in color image encryption.

Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

International Nuclear Information System (INIS)

Khaki-Sedigh, A.; Yazdanpanah-Goharrizi, A.

2006-01-01

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology

Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Khaki-Sedigh, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: sedigh@kntu.ac.ir; Yazdanpanah-Goharrizi, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: yazdanpanah@ee.kntu.ac.ir

2006-09-15

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology.

An image encryption scheme based on three-dimensional Brownian motion and chaotic system

International Nuclear Information System (INIS)

Chai Xiu-Li; Yuan Ke; Gan Zhi-Hua; Lu Yang; Chen Yi-Ran

2017-01-01

At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional (3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion (BCB3DBM) is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system (LTS). Furthermore, block confusion based on position sequence group (BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed. (paper)

Chaotic time series. Part II. System Identification and Prediction

Directory of Open Access Journals (Sweden)

Bjørn Lillekjendlie

1994-10-01

Full Text Available This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.

Controlling a Chaotic System through Control Parameter Self-Modulation

International Nuclear Information System (INIS)

Pastor, I.

1994-01-01

A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously existing unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and it is compared with them. One of its most attractive features is that it should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations modelling the coupling of two self-oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters

A New Scheme on Synchronization of Commensurate Fractional-Order Chaotic Systems Based on Lyapunov Equation

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Hua Wang

2016-01-01

Full Text Available This paper proposes a new fractional-order approach for synchronization of a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. A simple but practical method to synchronize many familiar fractional-order chaotic systems has been put forward. A new theorem is proposed for a class of cascade fractional-order systems and it is applied in chaos synchronization. Combined with the fact that the states of the fractional chaotic systems are bounded, many coupled items can be taken as zero items. Then, the whole system can be simplified greatly and a simpler controller can be derived. Finally, the validity of the presented scheme is illustrated by numerical simulations of the fractional-order unified system.

Chaos Q-S synchronization between Rossler system and the new unified chaotic system

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

In this Letter, we investigate the Q-S synchronization between two different chaotic systems: the Rossler system and the new unified Lorenz-Chen-Lu system based on the backstepping design method and Lyapunov stability theory. Moreover numerical simulations are used to verify the effectiveness of the proposed controller

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

Science.gov (United States)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-03-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems

International Nuclear Information System (INIS)

Poursamad, Amir; Markazi, Amir H.D.

2009-01-01

This paper describes an adaptive fuzzy sliding-mode control algorithm for controlling unknown or uncertain, multi-input multi-output (MIMO), possibly chaotic, dynamical systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal sliding-mode controller, and the robust controller compensates the difference between the fuzzy controller and the ideal one. The parameters of the fuzzy system, as well as the uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the asymptotic stability and tracking of the controlled system. The effectiveness of the proposed method is shown by applying it to some well-known chaotic systems.

Parameter estimation of Lorenz chaotic system using a hybrid swarm intelligence algorithm

International Nuclear Information System (INIS)

Lazzús, Juan A.; Rivera, Marco; López-Caraballo, Carlos H.

2016-01-01

A novel hybrid swarm intelligence algorithm for chaotic system parameter estimation is present. For this purpose, the parameters estimation on Lorenz systems is formulated as a multidimensional problem, and a hybrid approach based on particle swarm optimization with ant colony optimization (PSO–ACO) is implemented to solve this problem. Firstly, the performance of the proposed PSO–ACO algorithm is tested on a set of three representative benchmark functions, and the impact of the parameter settings on PSO–ACO efficiency is studied. Secondly, the parameter estimation is converted into an optimization problem on a three-dimensional Lorenz system. Numerical simulations on Lorenz model and comparisons with results obtained by other algorithms showed that PSO–ACO is a very powerful tool for parameter estimation with high accuracy and low deviations. - Highlights: • PSO–ACO combined particle swarm optimization with ant colony optimization. • This study is the first research of PSO–ACO to estimate parameters of chaotic systems. • PSO–ACO algorithm can identify the parameters of the three-dimensional Lorenz system with low deviations. • PSO–ACO is a very powerful tool for the parameter estimation on other chaotic system.

Parameter estimation of Lorenz chaotic system using a hybrid swarm intelligence algorithm

Energy Technology Data Exchange (ETDEWEB)

Lazzús, Juan A., E-mail: jlazzus@dfuls.cl; Rivera, Marco; López-Caraballo, Carlos H.

2016-03-11

A novel hybrid swarm intelligence algorithm for chaotic system parameter estimation is present. For this purpose, the parameters estimation on Lorenz systems is formulated as a multidimensional problem, and a hybrid approach based on particle swarm optimization with ant colony optimization (PSO–ACO) is implemented to solve this problem. Firstly, the performance of the proposed PSO–ACO algorithm is tested on a set of three representative benchmark functions, and the impact of the parameter settings on PSO–ACO efficiency is studied. Secondly, the parameter estimation is converted into an optimization problem on a three-dimensional Lorenz system. Numerical simulations on Lorenz model and comparisons with results obtained by other algorithms showed that PSO–ACO is a very powerful tool for parameter estimation with high accuracy and low deviations. - Highlights: • PSO–ACO combined particle swarm optimization with ant colony optimization. • This study is the first research of PSO–ACO to estimate parameters of chaotic systems. • PSO–ACO algorithm can identify the parameters of the three-dimensional Lorenz system with low deviations. • PSO–ACO is a very powerful tool for the parameter estimation on other chaotic system.

Two novel synchronization criterions for a unified chaotic system

International Nuclear Information System (INIS)

Tao Chaohai; Xiong Hongxia; Hu Feng

2006-01-01

Two novel synchronization criterions are proposed in this paper. It includes drive-response synchronization and adaptive synchronization schemes. Moreover, these synchronization criterions can be applied to a large class of chaotic systems and are very useful for secure communication

Nonlinear Dynamics, Chaotic and Complex Systems

Science.gov (United States)

Infeld, E.; Zelazny, R.; Galkowski, A.

2011-04-01

Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet

Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative

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Ping Zhou

2012-01-01

Full Text Available The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

Chaotic interactions of self-replicating RNA.

Science.gov (United States)

Forst, C V

1996-03-01

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

Comparison between different synchronization methods of identical chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Haeri, Mohammad [Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9363 Tehran (Iran, Islamic Republic of)]. E-mail: haeri@sina.sharif.edu; Khademian, Behzad [Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9363 Tehran (Iran, Islamic Republic of)

2006-08-15

This paper studies and compares three nonadaptive (bidirectional, unidirectional, and sliding mode) and two adaptive (active control and backstepping) synchronization methods on the synchronizing of four pairs of identical chaotic systems (Chua's circuit, Roessler system, Lorenz system, and Lue system). Results from computer simulations are presented in order to illustrate the effectiveness of the methods and to compare them based on different criteria.

An Application of Chaotic Chua's System for Secure Chaotic Communication Based on Sliding Mode observer

Science.gov (United States)

Kemih, K.; Halimi, M.; Ghanes, M.; Zhang, G.

2011-12-01

In this paper, we study the design and implementation of analog secure communication systems via synchronized chaotic Chua's circuit with sliding mode observer. For this, we adopt an approach based on an inclusion of the message in the transmitter and in the receiver; we use a sliding mode observer with un-known input in order to recover the information. Finally, an analog electronic circuit with Multisim software is designed to physically realize the complete system (transmitter-receiver).

A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps

International Nuclear Information System (INIS)

Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.

2007-01-01

In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security

A one-time pad color image cryptosystem based on SHA-3 and multiple chaotic systems

Science.gov (United States)

Wang, Xingyuan; Wang, Siwei; Zhang, Yingqian; Luo, Chao

2018-04-01

A novel image encryption algorithm is proposed that combines the SHA-3 hash function and two chaotic systems: the hyper-chaotic Lorenz and Chen systems. First, 384 bit keystream hash values are obtained by applying SHA-3 to plaintext. The sensitivity of the SHA-3 algorithm and chaotic systems ensures the effect of a one-time pad. Second, the color image is expanded into three-dimensional space. During permutation, it undergoes plane-plane displacements in the x, y and z dimensions. During diffusion, we use the adjacent pixel dataset and corresponding chaotic value to encrypt each pixel. Finally, the structure of alternating between permutation and diffusion is applied to enhance the level of security. Furthermore, we design techniques to improve the algorithm's encryption speed. Our experimental simulations show that the proposed cryptosystem achieves excellent encryption performance and can resist brute-force, statistical, and chosen-plaintext attacks.

Hybrid synchronization of two independent chaotic systems on ...

Indian Academy of Sciences (India)

The real network nodes are always interfered by other messages. So, how to realize the hybrid synchronization of two independent chaotic systems based on the complex network is very important. To solve this problem, two other problems should be considered. One is how the same network node of the complex network ...

Approximating chaotic saddles for delay differential equations.

Science.gov (United States)

Taylor, S Richard; Campbell, Sue Ann

2007-04-01

Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

Approximating chaotic saddles for delay differential equations

Science.gov (United States)

Taylor, S. Richard; Campbell, Sue Ann

2007-04-01

Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system

International Nuclear Information System (INIS)

Sudheer, K. Sebastian; Sabir, M.

2011-01-01

In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

THE ASTEROID BELT AS A RELIC FROM A CHAOTIC EARLY SOLAR SYSTEM

Energy Technology Data Exchange (ETDEWEB)

Izidoro, André; Raymond, Sean N.; Pierens, Arnaud [Laboratoire d’astrophysique de Bordeaux, Université de Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, F-33615 Pessac (France); Morbidelli, Alessandro [University of Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Laboratoire Lagrange, BP 4229, F-06304 Nice Cedex 4 (France); Winter, Othon C. [UNESP, Univ. Estadual Paulista—Grupo de Dinâmica Orbital and Planetologia, Guaratinguetá, CEP 12.516-410, São Paulo (Brazil); Nesvorny' , David, E-mail: izidoro.costa@gmail.com [Department of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302 (United States)

2016-12-10

The orbital structure of the asteroid belt holds a record of the solar system’s dynamical history. The current belt only contains ∼10{sup −3} Earth masses yet the asteroids’ orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter’s orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth’s orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter’s and Saturn’s early orbits were chaotic. Stochastic variations in the gas giants’ orbits cause resonances to continually jump across the main belt and excite the asteroids’ orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants’ current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.

Influences on the American Geographer Samuel Griswold Goodrich.

Science.gov (United States)

Smith, Ben A.; Vining, James W.

1989-01-01

Describes the influences of religion, upbringing, and other scholars on Samuel Griswold Goodrich, an early nineteenth-century U.S. geographer. Discusses Goodrich's contribution to improving early geography textbooks and his pioneering role in book publishing. Notes Goodrich's realism and moral undertones in geography books for children, written…

Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic.

Science.gov (United States)

Safonov, Leonid A.; Tomer, Elad; Strygin, Vadim V.; Ashkenazy, Yosef; Havlin, Shlomo

2002-12-01

We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.

A novel adaptive-impulsive synchronization of fractional-order chaotic systems

International Nuclear Information System (INIS)

Andrew, Leung Y. T.; Xian-Feng, Li; Yan-Dong, Chu; Hui, Zhang

2015-01-01

A novel adaptive–impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors’ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive–impulsive control scheme. (paper)

Parameter identification of Rossler's chaotic system by an evolutionary algorithm

Energy Technology Data Exchange (ETDEWEB)

Chang, W.-D. [Department of Computer and Communication, Shu-Te University, Kaohsiung 824, Taiwan (China)]. E-mail: wdchang@mail.stu.edu.tw

2006-09-15

In this paper, a differential evolution (DE) algorithm is applied to parameter identification of Rossler's chaotic system. The differential evolution has been shown to possess a powerful searching capability for finding the solutions for a given optimization problem, and it allows for parameter solution to appear directly in the form of floating point without further numerical coding or decoding. Three unknown parameters of Rossler's Chaotic system are optimally estimated by using the DE algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform

Science.gov (United States)

Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun

2018-07-01

Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.

Chaotic advection in the ocean

Energy Technology Data Exchange (ETDEWEB)

Koshel' , Konstantin V; Prants, Sergei V [V.I. Il' ichev Pacific Oceanological Institute, Far-Eastern Division of the Russian Academy of Sciences, Vladivostok (Russian Federation)

2006-11-30

The problem of chaotic advection of passive scalars in the ocean and its topological, dynamical, and fractal properties are considered from the standpoint of the theory of dynamical systems. Analytic and numerical results on Lagrangian transport and mixing in kinematic and dynamic chaotic advection models are described for meandering jet currents, topographical eddies in a barotropic ocean, and a two-layer baroclinic ocean. Laboratory experiments on hydrodynamic flows in rotating tanks as an imitation of geophysical chaotic advection are described. Perspectives of a dynamical system approach in physical oceanography are discussed. (reviews of topical problems)

Cryptanalysis of the public key encryption based on multiple chaotic systems

International Nuclear Information System (INIS)

Zhang Linhua

2008-01-01

Recently, Ranjan proposed a novel public key encryption technique based on multiple chaotic systems [Phys Lett 2005;95]. Unfortunately, Wang soon gave a successful attack on its special case based on Parseval's theorem [Wang K, Pei W, Zhou L, et al. Security of public key encryption technique based on multiple chaotic system. Phys Lett A, in press]. In this letter, we give an improved example which can avoid the attack and point out that Wang cannot find the essential drawback of the technique. However, further experimental result shows Ruanjan's encryption technique is inefficient, and detailed theoretic analysis shows that the complexity to break the cryptosystem is overestimated

Study on Unified Chaotic System-Based Wind Turbine Blade Fault Diagnostic System

Science.gov (United States)

Kuo, Ying-Che; Hsieh, Chin-Tsung; Yau, Her-Terng; Li, Yu-Chung

At present, vibration signals are processed and analyzed mostly in the frequency domain. The spectrum clearly shows the signal structure and the specific characteristic frequency band is analyzed, but the number of calculations required is huge, resulting in delays. Therefore, this study uses the characteristics of a nonlinear system to load the complete vibration signal to the unified chaotic system, applying the dynamic error to analyze the wind turbine vibration signal, and adopting extenics theory for artificial intelligent fault diagnosis of the analysis signal. Hence, a fault diagnostor has been developed for wind turbine rotating blades. This study simulates three wind turbine blade states, namely stress rupture, screw loosening and blade loss, and validates the methods. The experimental results prove that the unified chaotic system used in this paper has a significant effect on vibration signal analysis. Thus, the operating conditions of wind turbines can be quickly known from this fault diagnostic system, and the maintenance schedule can be arranged before the faults worsen, making the management and implementation of wind turbines smoother, so as to reduce many unnecessary costs.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

Science.gov (United States)

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Analysis, Adaptive Control and Anti-Synchronization of a Six-Term Novel Jerk Chaotic System with two Exponential Nonlinearities and its Circuit Simulation

Directory of Open Access Journals (Sweden)

S. Vaidyanathan

2014-11-01

Full Text Available This research work proposes a six-term novel 3-D jerk chaotic system with two exponential nonlinearities. This work also analyses system’s fundamental properties such as dissipativity, equilibria, Lyapunov exponents and Kaplan-Yorke dimension. The phase portraits of the jerk chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.24519, L2 = 0 and L3 = −0.84571. Also, the Kaplan-Yorke dimension of the novel jerk chaotic system is obtained as DKY = 2.2899. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system having two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global chaos anti-synchronization of two identical novel jerk chaotic systems with two unknown system parameters. Finally, an electronic circuit realization of the novel jerk chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.

Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series

Directory of Open Access Journals (Sweden)

Liu Hai

2015-01-01

Full Text Available Theoretic analysis shows that the output power of the distributed generation system is nonlinear and chaotic. And it is coupled with the microenvironment meteorological data. Chaos is an inherent property of nonlinear dynamic system. A predicator of the output power of the distributed generation system is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. Firstly, chaos should be detected and quantified for the intensive studies of nonlinear systems. If the largest Lyapunov exponent is positive, the dynamical system must be chaotic. Then, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. By now, the neural network can be trained based on the training samples, which are observed from the distributed generation system. The neural network model will approximate the curve of output power adequately. Experimental results show that the maximum power point of the distributed generation system will be predicted based on the meteorological data. The system can be controlled effectively based on the prediction.

Synchronization of the chaotic secure communication system with output state delay

International Nuclear Information System (INIS)

Changchien, S.-K.; Huang, C.-K.; Nien, H.-H.; Shieh, H.-W.

2009-01-01

In this paper, we utilize a proper Lyapunov function and Lyapunov theorem, combined with LMIs method, in order to design a controller L, which ensures the synchronization between the transmission and the reception ends of the chaotic secure communication system with time-delay of output state. Meanwhile, for the purpose of increasing communication security, we encrypt and decrypt the original to-be-transmitted message with the techniques of n-shift cipher and public key. The result of simulation shows that the proposed method is able to synchronize the transmission and the reception ends of the system, and moreover, to recover the original message at the reception end. Therefore, the method proposed in this paper is effective and feasible to apply in the chaotic secure communication system.

A note on chaotic synchronization of time-delay secure communication systems

International Nuclear Information System (INIS)

Li Demin; Wang Zidong; Zhou Jie; Fang Jianan; Ni Jinjin

2008-01-01

In a real world, the signals are often transmitted through a hostile environment, and therefore the secure communication system has attracted considerable research interests. In this paper, the observer-based chaotic synchronization problem is studied for a class of time-delay secure communication systems. The system under consideration is subject to delayed state and nonlinear disturbances. The time-delay is allowed to be time-varying, and the nonlinearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of a synchronization scheme such that, for the admissible time-delay as well as nonlinear disturbances, the response system can globally synchronize the driving system. An effective algebraic matrix inequality approach is developed to solve the chaotic synchronization problem. A numerical example is presented to show the effectiveness and efficiency of the proposed secure communication scheme

Analysis, Adaptive Control and Adaptive Synchronization of a Nine-Term Novel 3-D Chaotic System with Four Quadratic Nonlinearities and its Circuit Simulation

Directory of Open Access Journals (Sweden)

S. Vaidyanathan

2014-11-01

Full Text Available This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the 3-D novel chaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.

Sliding mode synchronization controller design with neural network for uncertain chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Mou Chen [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)], E-mail: chenmou@nuaa.edu.cn; Jiang Changsheng; Bin Jiang; Wu Qingxian [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)

2009-02-28

A sliding mode synchronization controller is presented with RBF neural network for two chaotic systems in this paper. The compound disturbance of the synchronization error system consists of nonlinear uncertainties and exterior disturbances of chaotic systems. Based on RBF neural networks, a compound disturbance observer is proposed and the update law of parameters is given to monitor the compound disturbance. The synchronization controller is given based on the output of the compound disturbance observer. The designed controller can make the synchronization error convergent to zero and overcome the disruption of the uncertainty and the exterior disturbance of the system. Finally, an example is given to demonstrate the availability of the proposed synchronization control method.

Anti-synchronization of two new different chaotic systems via active ...

African Journals Online (AJOL)

This paper investigates the anti-synchronization of chaos between two new different chaotic systems by using active control. Numerical simulations are used to show the robustness of the active control scheme in anti-synchronizing the two different coupled systems. JONAMP Vol. 11 2007: pp. 15-20 ...

A new type of chaotic synchronization with application to communication systems

International Nuclear Information System (INIS)

Kharel, Rupak; Busawon, Krishna

2011-01-01

In this paper, we propose a new methodology to synchronize a class of chaotic systems starting from different initial conditions under some given conditions. The method we propose is not based on the unidirectional synchronization method like the one proposed by Pecora-Caroll. The proposed method is unique in the sense that the chaotic oscillators to be synchronized have no direct connection between them; that is, there is no signal being sent from one to the other. Simulation result is presented to show the synchronization performance.

Modeling of memristor-based chaotic systems using nonlinear Wiener adaptive filters based on backslash operator

International Nuclear Information System (INIS)

Zhao, Yibo; Jiang, Yi; Feng, Jiuchao; Wu, Lifu

2016-01-01

Highlights: • A novel nonlinear Wiener adaptive filters based on the backslash operator are proposed. • The identification approach to the memristor-based chaotic systems using the proposed adaptive filters. • The weight update algorithm and convergence characteristics for the proposed adaptive filters are derived. - Abstract: Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.

Feedback control strategies for the Liu chaotic system

International Nuclear Information System (INIS)

Zhu Congxu; Chen Zhigang

2008-01-01

This Letter proposed three strategies of the dislocated feedback control, enhancing feedback control and speed feedback control of the Liu chaotic system to its unstable equilibrium points. It is found that the coefficients of enhancing feedback control and speed feedback control are smaller than those of ordinary feedback control, so, the complexity and cost of the system control are reduced. Theoretical analysis and numerical simulation are given, revealing the effectiveness of these strategies

An Approach of Tracking Control for Chaotic Systems

Directory of Open Access Journals (Sweden)

Jin Xing

2016-01-01

Full Text Available Combining the ergodicity of chaos and the Jacobian matrix, we design a general tracking controller for continuous and discrete chaotic systems. The control scheme has the ability to track a bounded reference signal. We prove its globally asymptotic stability and extend it to generalized projective synchronization. Numerical simulations verify the effectiveness of the proposed scheme.

Soul / Randy Becker, Bill Evans, Evelin Samuel ; interv. Sven Sapelson

Index Scriptorium Estoniae

Becker, Randy

2007-01-01

The Soulbop Bandi rajajad Randy Becker ja Bill Evans ning meie Evelin Samuel gospeli ja rhytmblues'i juurtega soulist. Lk. 72-73 Inessa Josingu ja Ande Kaalepi souliteemaline fotolavastusega ruumikujundus

A Novel Type of Chaotic Attractor for Quadratic Systems Without Equilibriums

Science.gov (United States)

Dantsev, Danylo

In this paper, a new chaotic dynamic system without equilibriums is presented. A conducted research of the qualitative properties of the discovered system reveals a noncompliance between the bifurcation behavior of the system and the Feigenbaum-Sharkovskii-Magnitsky theory. Additional research of known systems confirms the discrepancy.

Chaos synchronizations of chaotic systems via active nonlinear control

International Nuclear Information System (INIS)

Huang, J; Xiao, T J

2008-01-01

This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective

Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system

DEFF Research Database (Denmark)

Brøns, Morten; Sturis, Jeppe

2001-01-01

A model of an autocatalytic chemical reaction was employed to study the explosion of limit cycles and chaotic waves in a nonlinear chemical system. The bifurcation point was determined using asymptotic analysis and perturbations. Scaling laws for amplitude and period were derived. A strong sensit...... sensitivity was introduced due to bifurcation to infinity resulting in chaotic dynamics on adding diffusion....

O humano desumanizado num mundo sem sentido: Samuel Beckett e o herói absurdo = The dehumanized human being in a nonsense world: Samuel Beckett and the absurd hero

OpenAIRE

Maristela Kirst de Lima Girola

2011-01-01

Este ensaio tem como objetivo discutir a construção das personagens emEsperando Godot, de Samuel Beckett, apoiando-se nos estudos de Martin Esslin sobre o Teatro do Absurdo, uma forma de drama que enfatiza o absurdo da existência humana, empregando fragmentação, repetição e ininteligibilidade, como reação artística à Segunda Guerra Mundial.This essay discusses the construction of the characters in Waiting for Godot by Samuel Beckett, based on Martin Esslin’s studies on the Theatre of the Absu...

Unitarity and irreversibility in chaotic systems

International Nuclear Information System (INIS)

Hasegawa, H.H.; Saphir, W.C.

1992-01-01

We analyze the spectral properties of the Perron-Frobenius operator U, associated with some simple highly chaotic maps. We obtain a spectral decomposition of U in terms of generalized eigenfunctions of U and its adjoint. The corresponding eigenvalues are related to the decay rates of correlation functions and have magnitude less than one, so that physically measurable quantities manifestly approach equilibrium. To obtain decaying eigenstates of unitary and isometric operators it is necessary to extend the Hilbert-space formulation of dynamical systems. We describe and illustrate a method to obtain the decomposition explicitly

Controlling a Chaotic System through Control Parameter Self-Modulation

International Nuclear Information System (INIS)

Pastor, I.

1994-01-01

A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs

Controlling a Chaotic System through Control Parameter Self-Modulation

Energy Technology Data Exchange (ETDEWEB)

Pastor, I

1994-07-01

A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs.

Chaotic Behavior of a Generalized Sprott E Differential System

Science.gov (United States)

Oliveira, Regilene; Valls, Claudia

A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant b to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system ẋ = ayz + b,ẏ = x2 - y,ż = 1 - 4x, where a,b ∈ ℝ are parameters and a≠0. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in ℝ3 with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for b sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point p = (1/4, 1/16, 0). We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in ℝ3, and we show that it has no first integrals in the class of Darboux functions.

A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation

Science.gov (United States)

Rajagopal, Karthikeyan; Pham, Viet-Thanh; Tahir, Fadhil Rahma; Akgul, Akif; Abdolmohammadi, Hamid Reza; Jafari, Sajad

2018-04-01

The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.

Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system

Science.gov (United States)

Yu, Yue; Zhang, Zhengdi; Han, Xiujing

2018-03-01

In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.

Effect of Parametric Dichotomic Markov Noise on the Properties of Chaotic Transitions in Dynamical Systems

Science.gov (United States)

Gac, J. M.; Żebrowski, J. J.

A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in which a chaotic behavior occurs. The best known of these transitions are: the period-doubling bifurcation cascade, intermittency and crises. The effect of dichotomous Markov noise (DMN) on the properties of systems with chaotic transitions is discussed. DMN is a very simple two-valued stochastic process, with constant transition rates between the two states. In spite of its simplicity, this kind of noise is a very powerful tool to describe various phenomena present in many physical, chemical or biological systems. Many interesting phenomena induced by DMN are known. However, there is no research on the effect of this kind of noise on intermittency or crises. We present the change of the mean laminar phase length and of laminar phase length distribution caused by DMN modulating the parameters of a system with intermittency and the modification of the mean life time on the pre-crisis attractor in the case of a boundary crisis. The results obtained analytically are compared with numerical simulations for several simple dynamical systems.

On synchronisation of a class of complex chaotic systems with complex unknown parameters via integral sliding mode control

Science.gov (United States)

Tirandaz, Hamed; Karami-Mollaee, Ali

2018-06-01

Chaotic systems demonstrate complex behaviour in their state variables and their parameters, which generate some challenges and consequences. This paper presents a new synchronisation scheme based on integral sliding mode control (ISMC) method on a class of complex chaotic systems with complex unknown parameters. Synchronisation between corresponding states of a class of complex chaotic systems and also convergence of the errors of the system parameters to zero point are studied. The designed feedback control vector and complex unknown parameter vector are analytically achieved based on the Lyapunov stability theory. Moreover, the effectiveness of the proposed methodology is verified by synchronisation of the Chen complex system and the Lorenz complex systems as the leader and the follower chaotic systems, respectively. In conclusion, some numerical simulations related to the synchronisation methodology is given to illustrate the effectiveness of the theoretical discussions.

As Placas de Petri de Samuel

Directory of Open Access Journals (Sweden)

Araújo, Maria Valéria Pereira de

2014-12-01

Full Text Available The case teaching "The Petri dishes of Samuel" mentions a real situation occurred in a small business Medical Laboratory located in the city of Natal-RN. The dilemma of the case comes to a decision-making situation involving João, Director of the Laboratory Tércio Rosado and responsible for the human resources sector of the organization. The case is narrated from his point of view which faces a situation where one employee who works at the company for 25 years can not get adapted to the new technologies of the Medical Laboratory area, although the employee possesses behavioral and attitudinal competences which sets it apart from other professionals. After several attempts of training processes, trying to make Samuel adapt his behavior to the new technological requirements of the position, none of them were successful. Facing the situation the Director had a dilemma to solve: keep him in the company or not? If the company remains the employee, it might discourage the learning development of the other ones? On the other hand, the company would have other alternatives of training him in order to develop the required skills? What could be done? The case was constructed from observational data and informal conversations with employees and with the former owners of the company. Fictitious names were used to preserve the identity of the involved.

Regularized forecasting of chaotic dynamical systems

International Nuclear Information System (INIS)

Bollt, Erik M.

2017-01-01

While local models of dynamical systems have been highly successful in terms of using extensive data sets observing even a chaotic dynamical system to produce useful forecasts, there is a typical problem as follows. Specifically, with k-near neighbors, kNN method, local observations occur due to recurrences in a chaotic system, and this allows for local models to be built by regression to low dimensional polynomial approximations of the underlying system estimating a Taylor series. This has been a popular approach, particularly in context of scalar data observations which have been represented by time-delay embedding methods. However such local models can generally allow for spatial discontinuities of forecasts when considered globally, meaning jumps in predictions because the collected near neighbors vary from point to point. The source of these discontinuities is generally that the set of near neighbors varies discontinuously with respect to the position of the sample point, and so therefore does the model built from the near neighbors. It is possible to utilize local information inferred from near neighbors as usual but at the same time to impose a degree of regularity on a global scale. We present here a new global perspective extending the general local modeling concept. In so doing, then we proceed to show how this perspective allows us to impose prior presumed regularity into the model, by involving the Tikhonov regularity theory, since this classic perspective of optimization in ill-posed problems naturally balances fitting an objective with some prior assumed form of the result, such as continuity or derivative regularity for example. This all reduces to matrix manipulations which we demonstrate on a simple data set, with the implication that it may find much broader context.

On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system

International Nuclear Information System (INIS)

Zhou, Leilei; Chen, Zengqiang; Wang, Zhonglin; Wang, Jiezhi

2016-01-01

Highlights: • A new 4D smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented. • The stability of equilibria is observed near the bifurcation points. • The Hopf bifurcation and pitchfork bifurcation are analyzed by using the center manifold theorem and bifurcation theory. • A horseshoe with two-directional expansions in the 4D hyper-chaotic system has been found, which rigorously proves the existence of hyper-chaos in theory. - Abstract: In this paper, a new four-dimensional (4D) smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented and analyzed. The Lyapunov exponent (LE) spectrum, bifurcation diagram and various phase portraits of the system are provided. The stability, Hopf bifurcation and pitchfork bifurcation of equilibrium point are discussed by using the center manifold theorem and bifurcation theory. Numerical simulation results are consistent with the theoretical analysis. Besides, by combining the topological horseshoe theory with a computer-assisted method of Poincaré maps and utilizing the algorithm for finding horseshoes in 3D hyper-chaotic maps, a horseshoe with two-directional expansions in the 4D hyper-chaotic system is successfully found, which rigorously proves the existence of hyper-chaos in theory.

A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design

Directory of Open Access Journals (Sweden)

Qiang Lai

2017-12-01

Full Text Available This paper reports about a novel three-dimensional chaotic system with three nonlinearities. The system has one stable equilibrium, two stable equilibria and one saddle node, two saddle foci and one saddle node for different parameters. One salient feature of this novel system is its multiple attractors caused by different initial values. With the change of parameters, the system experiences mono-stability, bi-stability, mono-periodicity, bi-periodicity, one strange attractor, and two coexisting strange attractors. The complex dynamic behaviors of the system are revealed by analyzing the corresponding equilibria and using the numerical simulation method. In addition, an electronic circuit is given for implementing the chaotic attractors of the system. Using the new chaotic system, an S-Box is developed for cryptographic operations. Moreover, we test the performance of this produced S-Box and compare it to the existing S-Box studies.

A New Feigenbaum-Like Chaotic 3D System

Directory of Open Access Journals (Sweden)

Huitao Zhao

2014-01-01

Full Text Available Based on Sprott N system, a new three-dimensional autonomous system is reported. It is demonstrated to be chaotic in the sense of having positive largest Lyapunov exponent and fractional dimension. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcation diagram, Poincaré mapping, and period-doubling route to chaos are analyzed with careful numerical simulations. The obtained results also show that the period-doubling sequence of bifurcations leads to a Feigenbaum-like strange attractor.

A new transiently chaotic flow with ellipsoid equilibria

Science.gov (United States)

Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

2018-03-01

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

International Nuclear Information System (INIS)

Niu Yu-Jun; Pei Bing-Nan; Wang Xing-Yuan

2012-01-01

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor. (general)

Circuit implementation and multiform intermittency in a hyper-chaotic model extended from the Lorenz system

International Nuclear Information System (INIS)

Shi-Jian, Cang; Zeng-Qiang, Chen; Wen-Juan, Wu

2009-01-01

This paper presents a non-autonomous hyper-chaotic system, which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system. The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits, intermittency, chaos and hyper-chaos by controlling the frequency of the periodic signal. The phenomenon has been well demonstrated by numerical simulations, bifurcation analysis and electronic circuit realization. Moreover, the system is concrete evidence for the presence of Pomeau–Manneville Type-I intermittency and crisis-induced intermittency. The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing. By statistical analysis, power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states

A simple method of chaos control for a class of chaotic discrete-time systems

International Nuclear Information System (INIS)

Jiang Guoping; Zheng Weixing

2005-01-01

In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called 'odd eigenvalues number limitation' of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system

Robust synchronization of drive-response chaotic systems via adaptive sliding mode control

International Nuclear Information System (INIS)

Li, W.-L.; Chang, K.-M.

2009-01-01

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.

The adaptive synchronization of fractional-order Liu chaotic system ...

Indian Academy of Sciences (India)

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule ...

Study of chaos in chaotic satellite systems

Science.gov (United States)

Khan, Ayub; Kumar, Sanjay

2018-01-01

In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan-Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.

Studies in Chaotic adiabatic dynamics

International Nuclear Information System (INIS)

Jarzynski, C.

1994-01-01

Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)

GCS of a class of chaotic dynamic systems

International Nuclear Information System (INIS)

Park, Ju H.

2005-01-01

This article studies a guaranteed cost synchronization (GCS) problem for a class of chaotic systems. Attention is focused on the design of state feedback controllers such that the resulting closed-loop error system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) technique, two criteria for the existence of the controller for GCS are derived in terms of LMIs. To show the effectiveness of the proposed method, GCS problem of Genesio system verified by a numerical example

Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control

International Nuclear Information System (INIS)

Farivar, Faezeh; Aliyari Shoorehdeli, Mahdi; Nekoui, Mohammad Ali; Teshnehlab, Mohammad

2012-01-01

Highlights: ► A systematic procedure for GPS of unknown heavy chaotic gyroscope systems. ► Proposed methods are based on Lyapunov stability theory. ► Without calculating Lyapunov exponents and Eigen values of the Jacobian matrix. ► Capable to extend for a variety of chaotic systems. ► Useful for practical applications in the future. - Abstract: This paper proposes the chaos control and the generalized projective synchronization methods for heavy symmetric gyroscope systems via Gaussian radial basis adaptive variable structure control. Because of the nonlinear terms of the gyroscope system, the system exhibits chaotic motions. Occasionally, the extreme sensitivity to initial states in a system operating in chaotic mode can be very destructive to the system because of unpredictable behavior. In order to improve the performance of a dynamic system or avoid the chaotic phenomena, it is necessary to control a chaotic system with a periodic motion beneficial for working with a particular condition. As chaotic signals are usually broadband and noise like, synchronized chaotic systems can be used as cipher generators for secure communication. This paper presents chaos synchronization of two identical chaotic motions of symmetric gyroscopes. In this paper, the switching surfaces are adopted to ensure the stability of the error dynamics in variable structure control. Using the neural variable structure control technique, control laws are established which guarantees the chaos control and the generalized projective synchronization of unknown gyroscope systems. In the neural variable structure control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimator are derived in the sense of Lyapunov function. Thus, the unknown gyro systems can be guaranteed to be asymptotically stable. Also, the proposed method can achieve the control objectives. Numerical simulations are presented to

Dynamic analyses, FPGA implementation and engineering applications of multi-butterfly chaotic attractors generated from generalised Sprott C system

Science.gov (United States)

Lai, Qiang; Zhao, Xiao-Wen; Rajagopal, Karthikeyan; Xu, Guanghui; Akgul, Akif; Guleryuz, Emre

2018-01-01

This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found that the system creates two-, three-, four-, five-butterfly attractors and any other multi-butterfly attractors. First, the dynamic analyses of multi-butterfly chaotic attractors are presented. Secondly, the field programmable gate array implementation, electronic circuit realisation and random number generator are done with the multi-butterfly chaotic attractors.

Wada basins and chaotic invariant sets in the H non-Heiles system

CERN Document Server

Aguirre, J E; Sanjun, M A F

2001-01-01

The H non-Heiles Hamiltonian is investigated in the context of chaotic scattering, in the range of energies where escaping from the scattering region is possible. Special attention is paid to the analysis of the different nature of the orbits, and the invariant sets, such as the stable and unstable manifolds and the chaotic saddle. Furthermore, a discussion on the average decay time associated to the typical chaotic transients, which are present in this problem is presented. The main goal of this paper is to show, by using various computational methods, that the corresponding exit basins of this open Hamiltonian are not only fractal, but they also verify the more restrictive property of Wada. We argue that this property is verified by typical open Hamiltonian systems with three or more escapes.

Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

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Pablo César Rodríguez Gómez

2017-05-01

Full Text Available Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis. Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior. Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed. Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system. Language: English

Guaranteed cost control of time-delay chaotic systems

International Nuclear Information System (INIS)

Park, Ju H.; Kwon, O.M.

2006-01-01

This article studies a guaranteed cost control problem for a class of time-delay chaotic systems. Attention is focused on the design of memory state feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) framework, two criteria for the existence of the controller are derived in terms of LMIs. A numerical example is given to illustrate the proposed method

Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

International Nuclear Information System (INIS)

Jung, Jinwoo; Lee, Jewon; Song, Hanjung

2011-01-01

This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performed simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-μm single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with ±2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

Science.gov (United States)

Mobayen, Saleh

2018-06-01

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Collection of master-slave synchronized chaotic systems

International Nuclear Information System (INIS)

Lerescu, A.I.; Constandache, N.; Oancea, S.; Grosu, I.

2004-01-01

In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the systems that contains one nonlinear term and that term contains one variable then the coupling consists of one term. The numerical intervals of parameters where the synchronization is achieved are obtained analytically by applying Routh-Hurwitz conditions. Detailed calculations and numerical results are given for the system I from the Sprott's collection. Working in the same manner for many systems this method can be adopted for the teaching of the topic

Stochastic and Chaotic Relaxation Oscillations

NARCIS (Netherlands)

Grasman, J.; Roerdink, J.B.T.M.

1988-01-01

For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a

Routes to chaos in continuous mechanical systems: Part 2. Modelling transitions from regular to chaotic dynamics

International Nuclear Information System (INIS)

Krysko, A.V.; Awrejcewicz, J.; Papkova, I.V.; Krysko, V.A.

2012-01-01

In second part of the paper both classical and novel scenarios of transition from regular to chaotic dynamics of dissipative continuous mechanical systems are studied. A detailed analysis allowed us to detect the already known classical scenarios of transition from periodic to chaotic dynamics, and in particular the Feigenbaum scenario. The Feigenbaum constant was computed for all continuous mechanical objects studied in the first part of the paper. In addition, we illustrate and discuss different and novel scenarios of transition of the analysed systems from regular to chaotic dynamics, and we show that the type of scenario depends essentially on excitation parameters.

Chaotic Excitation and Tidal Damping in the GJ 876 System

Science.gov (United States)

Puranam, Abhijit; Batygin, Konstantin

2018-04-01

The M-dwarf GJ 876 is the closest known star to harbor a multi-planetary system. With three outer planets locked in a chaotic Laplace-type resonance and an appreciably eccentric short-period super-Earth, this system represents a unique exposition of extrasolar planetary dynamics. A key question that concerns the long-term evolution of this system, and the fate of close-in planets in general, is how the significant eccentricity of the inner-most planet is maintained against tidal circularization on timescales comparable to the age of the universe. Here, we employ stochastic secular perturbation theory and N-body simulations to show that the orbit of the inner-most planet is shaped by a delicate balance between extrinsic chaotic forcing and tidal dissipation. As such, the planet’s orbital eccentricity represents an indirect measure of its tidal quality factor. Based on the system’s present-day architecture, we estimate that the extrasolar super-Earth GJ 876 d has a tidal Q ∼ 104–105, a value characteristic of solar system gas giants.

Parameter estimation of fractional-order chaotic systems by using quantum parallel particle swarm optimization algorithm.

Directory of Open Access Journals (Sweden)

Yu Huang

Full Text Available Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.

Noise-Induced Riddling in Chaotic Systems

International Nuclear Information System (INIS)

Lai, Y.; Grebogi, C.

1996-01-01

Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise even if the attractor is transversely unstable, and we obtain universal scaling laws for noise-induced riddling. Our results imply that the phenomenon of riddling can be more prevalent than expected before, as noise is practically inevitable in dynamical systems. copyright 1996 The American Physical Society

Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system

Science.gov (United States)

Zhou, Nanrun; Chen, Weiwei; Yan, Xinyu; Wang, Yunqian

2018-06-01

In order to obtain higher encryption efficiency, a bit-level quantum color image encryption scheme by exploiting quantum cross-exchange operation and a 5D hyper-chaotic system is designed. Additionally, to enhance the scrambling effect, the quantum channel swapping operation is employed to swap the gray values of corresponding pixels. The proposed color image encryption algorithm has larger key space and higher security since the 5D hyper-chaotic system has more complex dynamic behavior, better randomness and unpredictability than those based on low-dimensional hyper-chaotic systems. Simulations and theoretical analyses demonstrate that the presented bit-level quantum color image encryption scheme outperforms its classical counterparts in efficiency and security.

Chaotic Dynamics and Transport in Classical and Quantum Systems

International Nuclear Information System (INIS)

2003-01-01

The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations

Chaotic Dynamics and Transport in Classical and Quantum Systems

Energy Technology Data Exchange (ETDEWEB)

NONE

2003-07-01

The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations.

Secure Image Encryption Based On a Chua Chaotic Noise Generator

Directory of Open Access Journals (Sweden)

A. S. Andreatos

2013-10-01

Full Text Available This paper presents a secure image cryptography telecom system based on a Chua's circuit chaotic noise generator. A chaotic system based on synchronised Master–Slave Chua's circuits has been used as a chaotic true random number generator (CTRNG. Chaotic systems present unpredictable and complex behaviour. This characteristic, together with the dependence on the initial conditions as well as the tolerance of the circuit components, make CTRNGs ideal for cryptography. In the proposed system, the transmitter mixes an input image with chaotic noise produced by a CTRNG. Using thresholding techniques, the chaotic signal is converted to a true random bit sequence. The receiver must be able to reproduce exactly the same chaotic noise in order to subtract it from the received signal. This becomes possible with synchronisation between the two Chua's circuits: through the use of specific techniques, the trajectory of the Slave chaotic system can be bound to that of the Master circuit producing (almost identical behaviour. Additional blocks have been used in order to make the system highly parameterisable and robust against common attacks. The whole system is simulated in Matlab. Simulation results demonstrate satisfactory performance, as well as, robustness against cryptanalysis. The system works with both greyscale and colour jpg images.

On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer

Directory of Open Access Journals (Sweden)

R. Idris

2013-01-01

Full Text Available A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.

Consistency properties of chaotic systems driven by time-delayed feedback

Science.gov (United States)

Jüngling, T.; Soriano, M. C.; Oliver, N.; Porte, X.; Fischer, I.

2018-04-01

Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the delay-driven laser and confirms the general theoretical results.

Complex network synchronization of chaotic systems with delay coupling

International Nuclear Information System (INIS)

Theesar, S. Jeeva Sathya; Ratnavelu, K.

2014-01-01

The study of complex networks enables us to understand the collective behavior of the interconnected elements and provides vast real time applications from biology to laser dynamics. In this paper, synchronization of complex network of chaotic systems has been studied. Every identical node in the complex network is assumed to be in Lur’e system form. In particular, delayed coupling has been assumed along with identical sector bounded nonlinear systems which are interconnected over network topology

Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique

International Nuclear Information System (INIS)

Peng, Y.-F.

2009-01-01

The cerebellar model articulation controller (CMAC) is a non-linear adaptive system with built-in simple computation, good generalization capability and fast learning property. In this paper, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive CMAC and H ∞ control technique is proposed for a class of chaotic systems with unknown system dynamics and external disturbance. In the proposed control system, an adaptive backstepping cerebellar model articulation controller (ABCMAC) is used to mimic an ideal backstepping control (IBC), and a robust H ∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. Moreover, the all adaptation laws of the RIBTC system are derived based on the Lyapunov stability analysis, the Taylor linearization technique and H ∞ control theory, so that the stability of the closed-loop system and H ∞ tracking performance can be guaranteed. Finally, three application examples, including a Duffing-Holmes chaotic system, a Genesio chaotic system and a Sprott circuit system, are used to demonstrate the effectiveness and performance of proposed robust control technique.

Control and switching synchronization of fractional order chaotic systems using active control technique

KAUST Repository

Radwan, A.G.; Moaddy, K.; Salama, Khaled N.; Momani, S.; Hashim, I.

2013-01-01

This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.

Control and switching synchronization of fractional order chaotic systems using active control technique

KAUST Repository

Radwan, A.G.

2013-03-13

This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.

Chaotic Behavior in a Switched Dynamical System

Directory of Open Access Journals (Sweden)

Fatima El Guezar

2008-01-01

Full Text Available We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator which is a Scilab (scientific laboratory package. The followed approach takes into account the hybrid nature of the circuit.

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

Directory of Open Access Journals (Sweden)

Shih-Yu Li

2015-01-01

Full Text Available A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1 apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2 a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3 three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

A New Fractional-Order Chaotic Complex System and Its Antisynchronization

Directory of Open Access Journals (Sweden)

Cuimei Jiang

2014-01-01

with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme.

A Dual Coding Theoretical Model of Decoding in Reading: Subsuming the LaBerge and Samuels Model

Science.gov (United States)

Sadoski, Mark; McTigue, Erin M.; Paivio, Allan

2012-01-01

In this article we present a detailed Dual Coding Theory (DCT) model of decoding. The DCT model reinterprets and subsumes The LaBerge and Samuels (1974) model of the reading process which has served well to account for decoding behaviors and the processes that underlie them. However, the LaBerge and Samuels model has had little to say about…

Comparison of different chaotic maps in particle swarm optimization algorithm for long-term cascaded hydroelectric system scheduling

International Nuclear Information System (INIS)

He Yaoyao; Zhou Jianzhong; Xiang Xiuqiao; Chen Heng; Qin Hui

2009-01-01

The goal of this paper is to present a novel chaotic particle swarm optimization (CPSO) algorithm and compares the efficiency of three one-dimensional chaotic maps within symmetrical region for long-term cascaded hydroelectric system scheduling. The introduced chaotic maps improve the global optimal capability of CPSO algorithm. Moreover, a piecewise linear interpolation function is employed to transform all constraints into restrict upriver water level for implementing the maximum of objective function. Numerical results and comparisons demonstrate the effect and speed of different algorithms on a practical hydro-system.

Security scheme in IMDD-OFDM-PON system with the chaotic pilot interval and scrambling

Science.gov (United States)

Chen, Qianghua; Bi, Meihua; Fu, Xiaosong; Lu, Yang; Zeng, Ran; Yang, Guowei; Yang, Xuelin; Xiao, Shilin

2018-01-01

In this paper, a random chaotic pilot interval and permutations scheme without any requirement of redundant sideband information is firstly proposed for the physical layer security-enhanced intensity modulation direct detection orthogonal frequency division multiplexing passive optical network (IMDD-OFDM-PON) system. With the help of the position feature of inserting the pilot, a simple logistic chaos map is used to generate the random pilot interval and scramble the chaotic subcarrier allocation of each column pilot data for improving the physical layer confidentiality. Due to the dynamic chaotic permutations of pilot data, the enhanced key space of ∼103303 is achieved in OFDM-PON. Moreover, the transmission experiment of 10-Gb/s 16-QAM encrypted OFDM data is successfully demonstrated over 20-km single-mode fiber, which indicates that the proposed scheme not only improves the system security, but also can achieve the same performance as in the common IMDD-OFDM-PON system without encryption scheme.

Una carta de pésame en arameo de Samuel ha-Naguid

Directory of Open Access Journals (Sweden)

Alba Cecilia, Amparo

2007-12-01

Full Text Available In this article we offer a Spanish translation with a commentary of an Aramaic letter of consolation written by Samuel ha-Naguid and sent to R. Ḥananel b. Ḥušiel, lamenting the death of R. Ḥušiel b. Elḥanán, his father.

En el presente artículo ofrecemos la traducción y el estudio de la carta de pésame enviada por Samuel ha-Naguid a R. Ḥananel b. Ḥušiel por la muerte de R. Ḥušiel b. Elḥanán, su padre.

Function projective lag synchronization of fractional-order chaotic systems

International Nuclear Information System (INIS)

Wang Sha; Yu Yong-Guang; Wang Hu; Rahmani Ahmed

2014-01-01

Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme. (general)

Data transmission system with encryption by chaotic sequences

Directory of Open Access Journals (Sweden)

Politans’kyy R. L.

2014-06-01

Full Text Available Protection of transferable information in the telecommunication systems is possible by its imposition of coding sequence on a plaintext. Encryption of pseudorandom sequences can be performed by using generation algorithms which are implemented on the basis of the phenomenon of dynamical chaos, which is sensitive to changes in the initial conditions. One of the major problems encountered in the construction of secure communication systems is to provide synchronization between the receiving and transmitting parties of communication systems. Improvement of methods of hidden data transfer based on the systems with chaotic synchronization is the important task of research in the field of information and telecommunication systems based on chaos. This article shows an implementation of a data transmission system, encrypted by sequences, generated on the basis of one-dimensional discrete chaotic maps with ensuring synchronization of the transmitting and receiving sides of the system. In this system realization of synchronization is offered by a transmission through certain time domains of current value of xn generated by a logistic reflection. Xn transmission period depends on computer speed and distance between subscribers of the system. Its value is determined by transmitting a test message before the session. Infallible reception of test message indicates the optimal choice of a transmission period of the current value of xn. Selection period is done at the program level. For the construction of communication network modern software was used, in particular programming language Delphi 7.0. The work of the system is shown on the example of information transmission between the users of the system. The system operates in real time full duplex mode at any hardware implementation of Internet access. It is enough for the users of the system to specify IP address only.

Robust function projective synchronization of a class of uncertain chaotic systems

International Nuclear Information System (INIS)

Shen Liqun; Liu Wanyu; Ma Jianwei

2009-01-01

In this paper, the function projective synchronization problem of chaotic systems is investigated, where parameter mismatch exists between the drive system and the response system. Based on Lyapunov stability theory, a novel robust function projective synchronization scheme is proposed. And the parameter mismatch problem is also solved. Simulation results of Lorenz system and Chen system verify the effectiveness of the proposed control scheme.

Security of public key encryption technique based on multiple chaotic systems

International Nuclear Information System (INIS)

Wang Kai; Pei Wenjiang; Zou Liuhua; Cheung Yiuming; He Zhenya

2006-01-01

Recently, a new public key encryption technique based on multiple chaotic systems has been proposed [B. Ranjan, Phys. Rev. Lett. 95 (2005) 098702]. This scheme employs m-chaotic systems and a set of linear functions for key exchange over an insecure channel. Security of the proposed algorithm grows as (NP) m , where N, P are the size of the key and the computational complexity of the linear functions respectively. In this Letter, the fundamental weakness of the cryptosystem is pointed out and a successful attack is described. Given the public keys and the initial vector, one can calculate the secret key based on Parseval's theorem. Both theoretical and experimental results show that the attacker can access to the secret key without difficulty. The lack of security discourages the use of such algorithm for practical applications

Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

KAUST Repository

N U+02BC Doye, Ibrahima

2018-02-13

In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

KAUST Repository

N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

2018-01-01

In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

Dynamics and Control of a Chaotic Electromagnetic System

OpenAIRE

Shun-Chang Chang

2012-01-01

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 simula...

Controller Synthesis for Periodically Forced Chaotic Systems

Science.gov (United States)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

Chaotic signals in digital communications

CERN Document Server

Eisencraft, Marcio; Suyama, Ricardo

2013-01-01

Chaotic Signals in Digital Communications combines fundamental background knowledge with state-of-the-art methods for using chaotic signals and systems in digital communications. The book builds a bridge between theoretical works and practical implementation to help researchers attain consistent performance in realistic environments. It shows the possible shortcomings of the chaos-based communication systems proposed in the literature, particularly when they are subjected to non-ideal conditions. It also presents a toolbox of techniques for researchers working to actually implement such system

Chaotic mechanics in systems with impacts and friction

CERN Document Server

Blazejczyk-Okolewska, Barbara; Kapitaniak, Tomasz; Wojewoda, Jerzy

1999-01-01

This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity - impacts and dry friction - are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field.

Synchronization of time-delayed systems with chaotic modulation and cryptography

International Nuclear Information System (INIS)

Banerjee, Santo

2009-01-01

This paper presents a method of synchronization between two time-delayed systems where the delay times are modulated by a common chaotic signal of the driving system. The technique is well applied to two identical autonomous continuous-time-delayed systems with numerical simulations. Finally, a new method of encryption is generated for digital messages. This method is illustrated with two different encryption processes for text as well as picture messages.

Ühe suve akvarellid / Evelin Samuel ja Liina Hergauk

Index Scriptorium Estoniae

Samuel, Evelin, 1975-

2015-01-01

Roosanupuline kampsun, idee ja teostus Evelin Samuel. Vanaroosa pluus ja barett, idee ja teostus Ruta Tännav. Mohäärlõngast topp, idee ja teostus Anna Verschik. Linane topp, idee ja teostus Liina Hergauk. Pitsmustritega mohäärkleit, idee ja teostus Ruta Tännav. Puuvillane topp, idee ja teostus Anna Verschik

Practical impulsive synchronization of chaotic systems with parametric uncertainty and mismatch

International Nuclear Information System (INIS)

Wen, C.Y.; Ji, Y.; Li, Z.G.

2007-01-01

Recently, there has been increasing interest in the synchronization of two chaotic systems and some significant results have been reported. In these results, a strong assumption that the two chaotic systems should be identical, i.e., without any mismatch, is imposed. Furthermore, system parameters are also assumed known exactly. Clearly, these are impractical. In this Letter, pure impulsive synchronization is considered. We quantitatively establish a relationship between a pre-specified bound of the synchronization error and the length of impulsive intervals in the presence of both parametric uncertainties and mismatch between the two systems. This is the first available result in the area, to the knowledge of the authors. With such a relationship as a guideline to choose impulsive intervals, a practical impulsive synchronization scheme is obtained. With the proposed scheme, the magnitude of the synchronization error is theoretically ensured to approach to and stay within the pre-specified bound which can be arbitrarily small. Simulation studies on the Lorenz system also verify the effectiveness of the proposed scheme

75 FR 27286 - McKelvie Geographic Area Range Allotment Management Planning on the Samuel R. McKelvie National...

Science.gov (United States)

2010-05-14

... range allotment management planning on the McKelvie Geographic Area, Samuel R. McKelvie National Forest... DEPARTMENT OF AGRICULTURE Forest Service McKelvie Geographic Area Range Allotment Management Planning on the Samuel R. McKelvie National Forest, Bessey Ranger District in Nebraska AGENCY: Forest...

Synchronization of Time-Continuous Chaotic Oscillators

DEFF Research Database (Denmark)

Yanchuk, S.; Maistrenko, Yuri; Mosekilde, Erik

2003-01-01

Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded...

Synchronization of linearly coupled unified chaotic systems based on linear balanced feedback scheme with constraints

International Nuclear Information System (INIS)

Chen, H.-H.; Chen, C.-S.; Lee, C.-I

2009-01-01

This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.

Quantization rules for strongly chaotic systems

International Nuclear Information System (INIS)

Aurich, R.; Bolte, J.

1992-09-01

We discuss the quantization of strongly chaotic systems and apply several quantization rules to a model system given by the unconstrained motion of a particle on a compact surface of constant negative Gaussian curvature. We study the periodic-orbit theory for distinct symmetry classes corresponding to a parity operation which is always present when such a surface has genus two. Recently, several quantization rules based on periodic orbit theory have been introduced. We compare quantizations using the dynamical zeta function Z(s) with the quantization condition cos(π N(E)) = 0, where a periodix-orbit expression for the spectral staircase N(E) is used. A general discussion of the efficiency of periodic-orbit quantization then allows us to compare the different methods. The system dependence of the efficiency, which is determined by the topological entropy τ and the mean level density anti d(E), is emphasized. (orig.)

Forward and adjoint sensitivity computation of chaotic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Qiqi, E-mail: qiqi@mit.edu [Department of Aeronautics and Astronautics, MIT, 77 Mass Ave., Cambridge, MA 02139 (United States)

2013-02-15

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.

Complex economic dynamics: Chaotic saddle, crisis and intermittency

International Nuclear Information System (INIS)

Chian, Abraham C.-L.; Rempel, Erico L.; Rogers, Colin

2006-01-01

Complex economic dynamics is studied by a forced oscillator model of business cycles. The technique of numerical modeling is applied to characterize the fundamental properties of complex economic systems which exhibit multiscale and multistability behaviors, as well as coexistence of order and chaos. In particular, we focus on the dynamics and structure of unstable periodic orbits and chaotic saddles within a periodic window of the bifurcation diagram, at the onset of a saddle-node bifurcation and of an attractor merging crisis, and in the chaotic regions associated with type-I intermittency and crisis-induced intermittency, in non-linear economic cycles. Inside a periodic window, chaotic saddles are responsible for the transient motion preceding convergence to a periodic or a chaotic attractor. The links between chaotic saddles, crisis and intermittency in complex economic dynamics are discussed. We show that a chaotic attractor is composed of chaotic saddles and unstable periodic orbits located in the gap regions of chaotic saddles. Non-linear modeling of economic chaotic saddle, crisis and intermittency can improve our understanding of the dynamics of financial intermittency observed in stock market and foreign exchange market. Characterization of the complex dynamics of economic systems is a powerful tool for pattern recognition and forecasting of business and financial cycles, as well as for optimization of management strategy and decision technology

Projective Synchronization of N-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

Directory of Open Access Journals (Sweden)

Baogui Xin

2012-01-01

Full Text Available Based on linear feedback control technique, a projective synchronization scheme of N-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

Nonlinear observer for synchronization of chaotic systems with application to secure data transmission

Science.gov (United States)

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Perez-Pinacho, Claudia A.

2014-06-01

The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.

Chaotic behavior learning of Chua's circuit

International Nuclear Information System (INIS)

Sun Jian-Cheng

2012-01-01

Least-square support vector machines (LS-SVM) are applied for learning the chaotic behavior of Chua's circuit. The system is divided into three multiple-input single-output (MISO) structures and the LS-SVM are trained individually. Comparing with classical approaches, the proposed one reduces the structural complexity and the selection of parameters is avoided. Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation. Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables, and exhibit the chaotic attractors under the autonomous working mode

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

Science.gov (United States)

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Nuclear friction and chaotic motion

International Nuclear Information System (INIS)

Srokowski, T.; Szczurek, A.; Drozdz, S.

1990-01-01

The concept of nuclear friction is considered from the point of view of regular versus chaotic motion in an atomic nucleus. Using a realistic nuclear Hamiltonian it is explicitly shown that the frictional description of the gross features of nuclear collisions is adequate if the system behaves chaotically. Because of the core in the Hamiltonian, the three-body nuclear system already reveals a structure of the phase space rich enough for this concept to be applicable

Modified Levenberg-Marquardt Method for RÖSSLER Chaotic System Fuzzy Modeling Training

Science.gov (United States)

Wang, Yu-Hui; Wu, Qing-Xian; Jiang, Chang-Sheng; Xue, Ya-Li; Fang, Wei

Generally, fuzzy approximation models require some human knowledge and experience. Operator's experience is involved in the mathematics of fuzzy theory as a collection of heuristic rules. The main goal of this paper is to present a new method for identifying unknown nonlinear dynamics such as Rössler system without any human knowledge. Instead of heuristic rules, the presented method uses the input-output data pairs to identify the Rössler chaotic system. The training algorithm is a modified Levenberg-Marquardt (L-M) method, which can adjust the parameters of each linear polynomial and fuzzy membership functions on line, and do not rely on experts' experience excessively. Finally, it is applied to training Rössler chaotic system fuzzy identification. Comparing this method with the standard L-M method, the convergence speed is accelerated. The simulation results demonstrate the effectiveness of the proposed method.

Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems

International Nuclear Information System (INIS)

Chang Weider; Yan Junjuh

2005-01-01

A robust adaptive PID controller design motivated from the sliding mode control is proposed for a class of uncertain chaotic systems in this paper. Three PID control gains, K p , K i , and K d , are adjustable parameters and will be updated online with an adequate adaptation mechanism to minimize a previously designed sliding condition. By introducing a supervisory controller, the stability of the closed-loop PID control system under with the plant uncertainty and external disturbance can be guaranteed. Finally, a well-known Duffing-Holmes chaotic system is used as an illustrative to show the effectiveness of the proposed robust adaptive PID controller

Chaotic dynamics and chaos control in nonlinear laser systems

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

2001-01-01

Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally

Identifying and Evaluating Chaotic Behavior in Hydro-Meteorological Processes

Directory of Open Access Journals (Sweden)

Soojun Kim

2015-01-01

Full Text Available The aim of this study is to identify and evaluate chaotic behavior in hydro-meteorological processes. This study poses the two hypotheses to identify chaotic behavior of the processes. First, assume that the input data is the significant factor to provide chaotic characteristics to output data. Second, assume that the system itself is the significant factor to provide chaotic characteristics to output data. For solving this issue, hydro-meteorological time series such as precipitation, air temperature, discharge, and storage volume were collected in the Great Salt Lake and Bear River Basin, USA. The time series in the period of approximately one year were extracted from the original series using the wavelet transform. The generated time series from summation of sine functions were fitted to each series and used for investigating the hypotheses. Then artificial neural networks had been built for modeling the reservoir system and the correlation dimension was analyzed for the evaluation of chaotic behavior between inputs and outputs. From the results, we found that the chaotic characteristic of the storage volume which is output is likely a byproduct of the chaotic behavior of the reservoir system itself rather than that of the input data.

Chaotic Music Generation System Using Music Conductor Gesture

OpenAIRE

Chen, Shuai; Maeda, Yoichiro; Takahashi, Yasutake

2013-01-01

In the research of interactive music generation, we propose a music generation method, that the computer generates the music, under the recognition of human music conductor's gestures.In this research, the generated music is tuned by the recognized gestures for the parameters of the network of chaotic elements in real time. The music conductor's hand motions are detected by Microsoft Kinect in this system. Music theories are embedded in the algorithm, as a result, the generated music will be ...

Transient Dynamics of Electric Power Systems: Direct Stability Assessment and Chaotic Motions

Science.gov (United States)

Chu, Chia-Chi

A power system is continuously experiencing disturbances. Analyzing, predicting, and controlling transient dynamics, which describe transient behaviors of the power system following disturbances, is a major concern in the planning and operation of a power utility. Important conclusions and decisions are made based on the result of system transient behaviors. As today's power network becomes highly interconnected and much more complex, it has become essential to enhance the fundamental understanding of transient dynamics, and to develop fast and reliable computational algorithms. In this thesis, we emphasize mathematical rigor rather than physical insight. Nonlinear dynamical system theory is applied to study two fundamental topics: direct stability assessment and chaotic motions. Conventionally, power system stability is determined by calculating the time-domain transient behaviors for a given disturbance. In contrast, direct methods identify whether or not the system will remain stable once the disturbance is removed by comparing the corresponding energy value of the post-fault system to a calculated threshold value. Direct methods not only avoid the time-consuming numerical integration of the time domain approach, but also provide a quantitative measure of the degree of system stability. We present a general framework for the theoretical foundations of direct methods. Canonical representations of network-reduction models as well as network-preserving models are proposed to facilitate the analysis and the construction of energy functions of various power system models. An advanced and practical method, called the boundary of stability region based controlling unstable equilibrium point method (BCU method), of computing the controlling unstable equilibrium point is proposed along with its theoretical foundation. Numerical solution algorithms capable of supporting on-line applications of direct methods are provided. Further possible improvements and enhancements are

Design of the Chaotic Signal Generator Based on LABVIEW

Directory of Open Access Journals (Sweden)

Jian-Guo Zhang

2014-01-01

Full Text Available We introduces a new method that can achieve the generation of Colpitts chaotic signal The system is based on virtual instrument platform and combined with MATLAB calculation to achieve the generation of Colpitts chaotic signal and making it analysis with autocorrelation and power spectrum at the same time. Signal channel output of chaotic signal was realized through USB-6009 acquisition module extending DA5405 high-speed DAC (Digital-to-Analog Converter chip. The system can adjust parameters based on customers’ requirements to achieve different frequency chaotic signal generation. Compared with the traditional autonomy Colpitts chaotic signal generator, this generator is simple and clear in structure, simple to operate, strong stability, easy to achieve etc.

New documents on Samuel Usque, the author of the Consolaçam as tribulaçoens de Israel

Directory of Open Access Journals (Sweden)

Guerrini, Maria Teresa

2001-06-01

Full Text Available Samuel Usque was a sixteenth-century Ferrara merchant and man of letters. Usque and Beatriz de Luna [Gracia Nasi] collaborated in the well-known task of reeducating Marranos in the precepts of normative Judaism. In addition, he represented Brianda Mendes in business trading in Antwerp, Ferrara, Venice and Ancona.Samuel Usque, literato y mercader en Ferrara en el siglo XVI, compartió con Beatriz de Luna [Gracia Nasi] el ya bien conocido proyecto cultural de la reeducación de los marranos en el judaismo. Además, Samuel Usque estuvo también al servicio de Brianda Méndez como mercader en Amberes, Ferrara, Venezia y Ancona.

Chaos Control in a New Three-Dimensional Chaotic T System

International Nuclear Information System (INIS)

Chen Yong; Yan Zhenya

2008-01-01

In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods (the linear, speed, doubly-periodic function controller) to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers

Theory and practice of chaotic cryptography

International Nuclear Information System (INIS)

Amigo, J.M.; Kocarev, L.; Szczepanski, J.

2007-01-01

In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography

Synchronization of complex chaotic systems in series expansion form

International Nuclear Information System (INIS)

Ge Zhengming; Yang Chenghsiung

2007-01-01

This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy

Alternative implementation of the chaotic Chen-Lee system

International Nuclear Information System (INIS)

Sheu, L.-J.; Tam, L.-M.; Chen, H.-K.; Lao, S.-K.

2009-01-01

The chaotic Chen-Lee system was developed with a formalism based on the Euler equations for the motion of a rigid body. It was proved that this system is the governing set of equations for gyro motion with feedback control. Recently, studies were conducted to explore the dynamic behavior of this system, including fractional order behavior, the generation of hyperchaos and perturbation analysis, control and anti-control of chaos, synchronization, etc. In this study, we further explore (1) the stability of the equilibrium points and (2) the implementation of an electronic circuit using the Chen-Lee system. It is shown that not only is this system related to gyro motion but can also be applied to electronic circuits for encryption purposes.

Design and Numerical Simulation of Unidirectional Chaotic Synchronization and its Application in Secure Communication System

Directory of Open Access Journals (Sweden)

A. Sambas

2013-09-01

Full Text Available Chaotic systems are characterized by sensitive dependence on initial conditions, similar to random behavior, and continuous broad-band power spectrum. Chaos is a good potential to be used in secure communications system. In this paper, in order to show some interesting phenomena of three-order Jerk circuit with modulus nonlinearity, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this paper is to analyze the phase portraits, the Poincaré maps, the bifurcation diagrams, while the analysis of the synchronization in the case of unidirectional coupling between two identical generated chaotic systems, has been presented. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the unidirectional coupling scheme between two identical Jerk circuits in a secure communication system is presented in details. Integration of theoretical physics, the numerical simulation by using MATLAB 2010, as well as the implementation of circuit simulations by using MultiSIM 10.0 has been performed in this study

Characterizing chaotic melodies in automatic music composition

Science.gov (United States)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Asynchronous error-correcting secure communication scheme based on fractional-order shifting chaotic system

Science.gov (United States)

Chao, Luo

2015-11-01

In this paper, a novel digital secure communication scheme is firstly proposed. Different from the usual secure communication schemes based on chaotic synchronization, the proposed scheme employs asynchronous communication which avoids the weakness of synchronous systems and is susceptible to environmental interference. Moreover, as to the transmission errors and data loss in the process of communication, the proposed scheme has the ability to be error-checking and error-correcting in real time. In order to guarantee security, the fractional-order complex chaotic system with the shifting of order is utilized to modulate the transmitted signal, which has high nonlinearity and complexity in both frequency and time domains. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the scheme.

O humano desumanizado num mundo sem sentido: Samuel Beckett e o herói absurdo = The dehumanized human being in a nonsense world: Samuel Beckett and the absurd hero

Directory of Open Access Journals (Sweden)

Maristela Kirst de Lima Girola

2011-01-01

Full Text Available Este ensaio tem como objetivo discutir a construção das personagens emEsperando Godot, de Samuel Beckett, apoiando-se nos estudos de Martin Esslin sobre o Teatro do Absurdo, uma forma de drama que enfatiza o absurdo da existência humana, empregando fragmentação, repetição e ininteligibilidade, como reação artística à Segunda Guerra Mundial.This essay discusses the construction of the characters in Waiting for Godot by Samuel Beckett, based on Martin Esslin’s studies on the Theatre of the Absurd, a form of drama that emphasizes the absurdity of human existence by employing split subjects, repetitions and meaninglessness as artistic reactions to World War II.

Stochastic perturbations in open chaotic systems: random versus noisy maps.

Science.gov (United States)

Bódai, Tamás; Altmann, Eduardo G; Endler, Antonio

2013-04-01

We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate κ and dimensions D of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of κ and D, and show that the improvement of the precision of the estimations with the number of trajectories N is extremely slow ([proportionality]1/lnN). We also argue that the finite-size D estimators are typically biased. General theoretical results are combined with analytical calculations and numerical simulations in area-preserving baker maps.

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

International Nuclear Information System (INIS)

Perez Polo, Manuel F.; Perez Molina, Manuel; Gil Chica, Javier

2009-01-01

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

Energy Technology Data Exchange (ETDEWEB)

Perez Polo, Manuel F. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia. UNED, C/Boyero 12-1A, Alicante 03007 (Spain)], E-mail: ma_perez_m@hotmail.com; Gil Chica, Javier [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: gil@dfists.ua.es

2009-02-15

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.

Regular transport dynamics produce chaotic travel times.

Science.gov (United States)

Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro

2014-06-01

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

Chaos control for a class of chaotic systems using PI-type state observer approach

International Nuclear Information System (INIS)

Jiang Guoping; Zheng Weixing

2004-01-01

In this paper, by using the PI-type state observer design approach and the characteristic of ergodicity of chaos, a new method is presented for controlling chaos, including the stabilization of unstable equilibrium points and set-point tracking, for a class of chaotic systems. Based on the theory of nonlinear ordinary differential equations, a simple criterion is derived for designing the controller gains for stabilization and tracking, in which control parameters can be selected via the pole placement technique of linear control theory. More importantly, this control method has a simple controller structure, high robustness against system parametric variations, and strong rejection of external constant disturbances. The method is applied to the chaotic Lorenz system for demonstration

Does the classically chaotic Henon–Heiles oscillator exhibit ...

Indian Academy of Sciences (India)

–12]. In contrast to a classically chaotic system, where the exponential divergence of trajectories in phase-space is an unambiguous and confirmatory signature of chaos. [15–17], the decision about whether a quantum system is chaotic or not is ...

Novel adaptive feedback synchronization scheme for a class of chaotic systems with and without parametric uncertainty

International Nuclear Information System (INIS)

Handa, Himesh; Sharma, B.B.

2016-01-01

Highlights: • New adaptive control design strategy to address chaotic system synchronization in master-slave configuration. • To derive control structure using model reference adaptive control like approach. • Extension of results to address general case with known and unknown system parameters. • Application of proposed strategy to chaotic systems. - Abstract: In this paper, a new adaptive feedback control design technique for the synchronization of a class of chaotic systems in master–slave configuration is proposed. The controller parameters are assumed to be unknown and are evolved using adaptation laws so as to achieve synchronization. To replicate real system operation, uncertainties are considered in both master as well as salve system parameters and adaptation laws for uncertain parameters are analytically derived using Lyapunov stability theory. The proposed strategy is derived by mimicking model reference adaptive control like structure for synchronization problem. To validate the methodology, two Genesio–Tesi systems and two Rossler's Prototype-4 systems are considered in master–slave configuration for synchronization. The analysis is done first with known system parameters and then uncertainties in system parameters are considered. Finally, detailed simulation results are provided to illustrate the effectiveness of the proposed results.

Image Encryption and Chaotic Cellular Neural Network

Science.gov (United States)

Peng, Jun; Zhang, Du

Machine learning has been playing an increasingly important role in information security and assurance. One of the areas of new applications is to design cryptographic systems by using chaotic neural network due to the fact that chaotic systems have several appealing features for information security applications. In this chapter, we describe a novel image encryption algorithm that is based on a chaotic cellular neural network. We start by giving an introduction to the concept of image encryption and its main technologies, and an overview of the chaotic cellular neural network. We then discuss the proposed image encryption algorithm in details, which is followed by a number of security analyses (key space analysis, sensitivity analysis, information entropy analysis and statistical analysis). The comparison with the most recently reported chaos-based image encryption algorithms indicates that the algorithm proposed in this chapter has a better security performance. Finally, we conclude the chapter with possible future work and application prospects of the chaotic cellular neural network in other information assurance and security areas.

Hypogenetic chaotic jerk flows

International Nuclear Information System (INIS)

Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan

2016-01-01

Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications. - Highlights: • Hypogenetic chaotic jerk flows with incomplete feedback of amplitude or polarity are obtained. • Multistability of symmetric coexisting attractors from an asymmetric structure is found. • Some jerk systems have hidden attractors with respect to equilibria but have global attraction. • These chaotic jerk flows have the properties of amplitude control and phase reversal.

A New Simple Chaotic Circuit Based on Memristor

Science.gov (United States)

Wu, Renping; Wang, Chunhua

In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage-current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost.

Anti-Synchronization of Chaotic Systems via Adaptive Sliding Mode Control

International Nuclear Information System (INIS)

Jawaada, Wafaa; Noorani, M. S. M.; Al-Sawalha, M. Mossa

2012-01-01

An anti-synchronization scheme is proposed to achieve the anti-synchronization behavior between chaotic systems with fully unknown parameters. A sliding surface and an adaptive sliding mode controller are designed to gain the anti-synchronization. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally numerical results are presented to justify the theoretical analysis

Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems

International Nuclear Information System (INIS)

Peng Yafu

2009-01-01

In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua's chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system

The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system

International Nuclear Information System (INIS)

Waldner, Franz; Hoover, William G.; Hoover, Carol G.

2014-01-01

Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed

Parameter identification technique for uncertain chaotic systems using state feedback and steady-state analysis.

Science.gov (United States)

Zaher, Ashraf A

2008-03-01

A technique is introduced for identifying uncertain and/or unknown parameters of chaotic dynamical systems via using simple state feedback. The proposed technique is based on bringing the system into a stable steady state and then solving for the unknown parameters using a simple algebraic method that requires access to the complete or partial states of the system depending on the dynamical model of the chaotic system. The choice of the state feedback is optimized in terms of practicality and causality via employing a single feedback signal and tuning the feedback gain to ensure both stability and identifiability. The case when only a single scalar time series of one of the states is available is also considered and it is demonstrated that a synchronization-based state observer can be augmented to the state feedback to address this problem. A detailed case study using the Lorenz system is used to exemplify the suggested technique. In addition, both the Rössler and Chua systems are examined as possible candidates for utilizing the proposed methodology when partial identification of the unknown parameters is considered. Finally, the dependence of the proposed technique on the structure of the chaotic dynamical model and the operating conditions is discussed and its advantages and limitations are highlighted via comparing it with other methods reported in the literature.

Synchronization of integral and fractional order chaotic systems a differential algebraic and differential geometric approach with selected applications in real-time

CERN Document Server

Martínez-Guerra, Rafael; Gómez-Cortés, Gian Carlo

2015-01-01

This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only...

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

Science.gov (United States)

Hajipour, Ahmad; Tavakoli, Hamidreza

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

Science.gov (United States)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Analytically solvable chaotic oscillator based on a first-order filter

Energy Technology Data Exchange (ETDEWEB)

Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N. [Charles M. Bowden Laboratory, Aviation and Missile Research, Development and Engineering Center, U.S. Army RDECOM, Redstone Arsenal, Alabama 35898 (United States)

2016-02-15

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

Chaotic Zones around Rotating Small Bodies

Energy Technology Data Exchange (ETDEWEB)

Lages, José; Shevchenko, Ivan I. [Institut UTINAM, Observatoire des Sciences de l’Univers THETA, CNRS, Université de Franche-Comté, Besançon F-25030 (France); Shepelyansky, Dima L., E-mail: jose.lages@utinam.cnrs.fr [Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, Toulouse F-31062 (France)

2017-06-01

Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumb-bells or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples of the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.

A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

Energy Technology Data Exchange (ETDEWEB)

Castro-Ramírez, Joel, E-mail: ingcastro.7@gmail.com [Universidad Politécnica de Tlaxcala Av. Universidad Politecnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico); Martínez-Guerra, Rafael, E-mail: rguerra@ctrl.cinvestav.mx [Departamento de Control Automático CINVESTAV-IPN, A.P. 14-740, D.F., México C.P. 07360 (Mexico); Cruz-Victoria, Juan Crescenciano, E-mail: juancrescenciano.cruz@uptlax.edu.mx [Universidad Politécnica de Tlaxcala Av. Universidad Politécnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico)

2015-10-15

This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.

A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

International Nuclear Information System (INIS)

Castro-Ramírez, Joel; Martínez-Guerra, Rafael; Cruz-Victoria, Juan Crescenciano

2015-01-01

This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system

Chaos suppression based on adaptive observer for a P-class of chaotic systems

International Nuclear Information System (INIS)

Rodriguez, Angel; Leon, Jesus de; Femat, Ricardo

2007-01-01

A feedback approach is presented to suppress chaos in a P-class of chaotic system. The approach is based on an adaptive observer; which provides estimated values of both the unmeasured states and the uncertain model parameters. A continuous-time feedback law is taken as suppressing force. The feedback law attains chaos suppression as the observer provides estimated values close to the actual state/parameter values along time. The proposed scheme is robust in the sense that suppression is achieved despite only some states are measured and uncertainties in parameters are compensated. Results are corroborated experimentally by implementation in chaotic circuits

Chaos suppression based on adaptive observer for a P-class of chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Rodriguez, Angel [Universidad Autonoma de Nuevo Leon, Facultad de Ingenieria Mecanica y Electrica, Av. Pedro de Alba s/n Cd. Universitaria, CP 66450 San Nicolas de los Garza, NL (Mexico); Leon, Jesus de [Universidad Autonoma de Nuevo Leon, Facultad de Ingenieria Mecanica y Electrica, Av. Pedro de Alba s/n Cd. Universitaria, CP 66450 San Nicolas de los Garza, NL (Mexico); Femat, Ricardo [Division de Matematicas Aplicadas y Sistemas Computacionales, IPICyT, Camino a la Presa San Jose 2055 Col. Lomas 4a. Secc. CP 78216 San Luis Potosi, SLP (Mexico)]. E-mail: rfemat@ipicyt.edu.mx

2007-05-15

A feedback approach is presented to suppress chaos in a P-class of chaotic system. The approach is based on an adaptive observer; which provides estimated values of both the unmeasured states and the uncertain model parameters. A continuous-time feedback law is taken as suppressing force. The feedback law attains chaos suppression as the observer provides estimated values close to the actual state/parameter values along time. The proposed scheme is robust in the sense that suppression is achieved despite only some states are measured and uncertainties in parameters are compensated. Results are corroborated experimentally by implementation in chaotic circuits.

Mental Self-Exploration in Samuel Beckett's "Molloy": A Jungian Approach