Chaotic dynamical systems have potential applications in communications and signal processing. The definition of finitetime generalized synchronization is put forward for the first time. Fractional order control and synchronization of chaotic. Early work on synchronous, coupled chaotic systems was done by. We have demonstrated in simulations that chaotic systems can be synchronized and this. Fundamentals of synchronization in chaotic systems, concepts. Chaotic communication based on the gs has been studied in 2123.
Chaotic synchronization, symbolic dynamics, symbolic synchronization, kneading theory. Adaptive synchronization of chaotic systems and its application to. This paper demonstrates the use of lyapunov direct method in synchronizing two identical lorenzstenflo ls systems, two identical qi systems and two nonidentical systems comprising the ls and qi chaotic systems. Chaotic systems synchronization in secure communication systems ahmad m. Dec 08, 2020 this paper investigates the partial anti synchronization in a class of chaotic and hyper chaotic systems. Recent advances in chaotic systems and synchronization. One characteristic of a chaotic system is that the signals produced by a chaotic system do not synchronize with any other system. However, the existing synchronization has been acquired for two chaotic systems, and the synchronization problems of n chaotic systems are yet to be investigated. The numerical results presented show the effectiveness of the. Adaptive synchronization of chaotic systems and its. Code 6341, naval research laboratory, washington, d. Jun 21, 20 synchronization is ubiquitous in nature.
The synchronization and lack of synchronization of several wellstudied chaotic systems is reexplained in these terms. Fractional order control and synchronization of chaotic systems. In more development point of view, huang studied the chaos. Although a chaotic system can have a pattern an attractor. Synchronization of a threedimensional chaotic finance. As far as the conditional lyapunov exponents between the transmitter and receiver systems have negative values, we can achieve chaos synchronization. Synchronization analysis of a new autonomous chaotic system.
Hence, the parallel system of a chaotic system is also chaotic. Coexistence of synchronization and antisynchronization in chaotic. The master system and slave systems have uncertainties and external disturbances. Recent advances in chaotic systems and synchronization 1st. We modify this method for the case of the drive and response system. Firstly, the existence of the partial anti synchronization for the chaotic system is proved. We have demonstrated in simulations that chaotic systems can. Synchronization of chaos is a phenomenon that may occur when two, or more, dissipative chaotic systems are coupled. Pdf synchronization in chaotic systems, concepts and applications. The controller was applied to synchronize the chen chaotic system with the. Modeling and synchronizing chaotic systems from time. Synchronization of chaos refers to a process wherein two or many chaotic systems either equivalent or nonequivalent adjust a given property of their motion to a common behavior due to a.
Fundamentals of synchronization in chaotic systems, concepts, and. Pdf synchronization of different chaotic systems and. We will use both the modified fy and the pc method to accomplish the synchronization. Furthermore, as the number of chaotic systems decreases from n to 2, the proposed synchronization will transform into bidirectional coupling synchronization. In this paper, the generalized synchronization of chaotic systems with different order is studied.
Synchronization of chaotic systems and transmission of. Pdf synchronization in chaotic system researchgate. By a linear controller, we realize the dual synchronization of fractionalorder chaotic systems. Simple adaptive synchronization of chaotic systems with random components chaos 16, 023128 2006. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as. For example, yassen 11 studied the synchronization problem of different uni. Dual synchronization of fractionalorder chaotic systems. A fuzzy statefeedback controller using the system state of response chaotic system and the timedelayed system state of drive chaotic system is employed to realize the synchronization. In this paper, new results are derived for the anti synchronization of identical liuchen fourscroll chaotic systems liu and chen, 2004 and identical luchen cheng fourscroll chaotic systems lu,chen and cheng, 2004 by sliding mode control. Synchronization in chaotic dynamical systems diva portal. Abstract synchronization of chaos refers to a process wherein two or many chaotic systems either equivalent or nonequivalent adjust a given property of their motion to a common behavior due to.
Moreover, all parameters of chaotic system must be known in advance. Conclusion a new controllersynchronizer was designed for the chen chaotic system. This books report on the latest developments and applications of fractional order control and synchronization of disordered systems explains the concepts of a clear and realistic style. A new method for synchronization and control of the chen. Finite time stability and synchronization of fractional order chaotic system with uncertainties and disturbance was studied in 17. For the given chaotic system 4, we construct a new system as 5 w. In fact, the synchronization for two chaotic systems can be defined as the following two types.
In this paper, we investigate a novel synchronization method, which consists of n cascadecoupled chaotic systems. Jestr engineering science and special issue on recent. Accurate synchronization of digital and analog chaotic. Synchronization analysis of a new autonomous chaotic. First, the notion of synchronization is discussed, then the coupling of two systems to achieve synchronization is presented and then four methods to mix the information signal with a chaotic carrier are described. So it is important to design gs for chaotic systems in view of the potential ap. Using the concept of synchronized chaotic systems scss, two possible approaches to secure communications are demonstrated with the. Fractionalorder differential equations fdes, chaos, coullet system. The results are validated using numerical simulations.
The stability of adaptive synchronization of chaotic systems. Unidirectional chaotic synchronization of rossler circuit and. Linear generalized synchronization of continuoustime. The problem of the dual synchronization of two different fractionalorder chaotic systems is studied. Recently chaos is found to be useful in many fields. Although chaotic synchronization can be ensured due to the effect of transmitting the nonlinear terms, the. A reapproach to chaotic systems synchronization is presented from the perspective of passivitybased state observer design in the context of generalized hamiltonian systems including dissipation and destabilizing vector fields. Because chaotic signals are noiselike and difficult to predict. Synchronization of chaotic systems lincoln repository. Now, our goal is to make synchronization for two identical chaotic systems of the form 1 based on the lyapunov method.
Based on lyapunov stability theory, a general criterion is proposed for choosing the appropriate coupling. We are asking physical and dynamical ques tions regarding synchronized, chaotic states. This paper presents the use of active disturbance rejection control method adrc to synchronize two different chaotic systems. Chaos synchronization and chaotic signal masking in. Synchronization of different chaotic systems and electronic. This survey provides an introduction to the phenomenon of synchronisation in coupled chaotic dynamical systems. Modeling and synchronizing chaotic systems from timeseries data. Control and synchronization of chaotic fractionalorder. Chaos synchronization of a chaotic system via nonlinear. An overview over the methods currently under investigation for the transmission of information hidden in a chaotic signal is given. Synchronization of chaotic systems journal article osti. Pdf synchronization of identical and nonidentical 4d.
Synchronization of a threedimensional chaotic finance system. Introduction synchronization of two or more systems, is a process wherein the systems adjust a given property of their motion to a common behaviour, due to coupling or forcing. Pdf, the synchronization of chaotic systems applying. The controller made use of a new adaptation law for its parameter adjustment. The stability of synchronization for coupled systems can be analy.
This is usually couched mathematically as a sensitivity to initial conditionswhere the system s dynamics takes it is hard to predict from the starting point. The combination of inphase and antiphase synchronization provides a way to encode messages into an array of synchronous chaotic sys. The time delay which complicates the system dynamics makes the analysis difficult. From theory to real world applications is a major reference for scientists and engineers interested in applying new computational and mathematical tools for solving complex problems related to modeling, analyzing and synchronizing chaotic systems. The synchronization of chaotic systems request pdf. Pdf introduction and motivationthe geometry of synchronization simple. Because of the exponential divergence of the nearby trajectories of chaotic systems, having two chaotic systems evolving in synchrony might appear surprising. Chaos synchronization is the agreement or correlation of. The convergence of the two systems to identical trajectories is a surprise. Strogatz abstruct a circuit implementation of the chaotic lorenz system is described.
The stability of synchronization for coupled systems. In our study, we propose a hybrid technique for chaotic systems identification, based on the chaotic synchronization. Note that fy have considered the synchronization of chaotic oscillators with mutual coupling. However, synchronization of coupled or driven chaotic oscillators is a phenomenon well established experimentally and reasonably wellunderstood theoretically. This phenomenon has been the basis for proposals for secure communication,46 system identi. In our scheme, synchronization can be readily achieved even when the system has more than one positive lyapunov exponent hyperchaotic iii. Chaotic systems can synchronize chaos has longterm unpredictable behavior. Fundamentals of synchronization in chaotic systems. Synchronization of extended chaotic systems scholarpedia. Synchronization, nonlinear control, active control.
Finally, the problem to send several information bearing chaotic signals through the same communication channel is posed as a challenge. Department of quantitative methods, iscteiul portugal 1 2 3 emails. Synchronization of lorenzbased chaotic circuits with. To the best of our knowledge, this has not been previously reported. The chaos synchronization between genesio chaotic systems with noise perturbation was reported in 18. Phase synchronization in regular and chaotic systems 2293 if the rotation number is rational, the observed frequency is in the rational relation with the frequency of the external force. In semiconductor laser systems, chaotic secure communi. As synchronization based communication schemes, chaotic signal masking and chaotic modulation 7,8. Strogatz abstruct a circuit implementation of the chaotic lorenz.
Linear generalized synchronization of continuoustime chaotic. This innovation provided a new perspective in chaotic dynamics and inspired many studies on the synchronization of chaotic systems. Based on the finitetime stability theory, two control strategies are proposed to realize the generalized synchronization of chaotic systems with different order in finite time. Apr 16, 2015 in this paper, he starts with a dynamical system chaotic or not, x. Pdf synchronization of chaotic dynamical systems rosario.
Chaos synchronization of a chaotic system via nonlinear control. Remarkably, all these different phenomena can be described within the common framework of nonlinear dynamics pikovsky et al, 2001. Aug 01, 2007 in this paper, the chaotic synchronization refers to the complete synchronization, and it means that the difference of the states of two relevant systems will converge to zero. This paper investigates the partial anti synchronization in a class of chaotic and hyper chaotic systems.
Adaptive fuzzy logic controller flc equipped with an adaptive algorithm to achieve h. Pecora and carroll first demonstrated how chaotic systems could be synchronized, using an electronic circuit coupled unidirectional to a subsystem made up of components of the parent system 22. On global synchronization of chaotic systems ieee xplore. Finitetime generalized synchronization of chaotic systems. Although chaotic synchronization can be ensured due to the eect of transmitting the nonlinear terms, the implementation of nonlinear functions is more complicated in practice. Synchronization of chaotic systems via active disturbance. The synchronization of n cascadecoupled chaotic systems. Synchronization for chaotic dynamical systems springerlink.
Jun 04, 1998 arrays of coupled chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuitive phenomena including bursting above synchronization thresholds, destabilizing transitions as coupling increases shortwavelength bifurcations, and riddled basins. All mentioned studies are done either experimentally or using state feedback linear control. Synchronization and antisynchronization for chaotic systems. The robustness for communications and the allowance for parameter mismatches between the two systems are important issues in chaos communications based on chaos synchronization and such studies have been conducted 12, 55, 59. Transverse stability of trajectories in invariant manifolds. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. Synchronization of chen chaotic system with an arbitrary reference shows the flexibility of the controller. An introduction to the synchronization of chaotic systems. The impulsive control method is used to control synchronization of the chaotic. Robust adaptive synchronization of a class of uncertain chaotic.
The designed controllers enable the state variables of the slave system to globally synchronize with the state variables of the master system in both the identical and nonidentical systems. Chaos synchronization has potential applications in secure communication and other applications. Chaos is a complex nonlinear phenomenon which is intensively studied over the past two decades within science, mathematics and engineering communities. Dual synchronization of fractionalorder chaotic systems via.
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