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Synchronization of extended chaotic systems

Alessandro Torcini, Massimo Cencini
2013 Scholarpedia  
Low Dimensional Chaotic Systems Chaotic Dynamicṡ u k (t) = ϕ k (u(t)) k = 1, 2, 3, . . . maximum Lyapunov exponent λ > 0 Mutually Coupled Systems Two replicas u and w of the same dynamical system: u  ...  [Ginelli,Livi,Politi, & AT PRE 67, 046217 (2003) ] Summary of the first part In spatially extended systems (CMLs) with diffusive coupling two different synchronization transitions are observed : if  ...  Field Theoretic Prediction The generalization of the usual field equation to anomalous DP reads as: where η is a Gaussian noise δ-correlated in space and the anomalous diffusion operator is defined as  ... 
doi:10.4249/scholarpedia.30650 fatcat:tweecs5hrrb2pl37zweow7s3yi

Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

M. Cencini, C. J. Tessone, A. Torcini
2008 Chaos  
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength.  ...  As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via power-law coupling is considered.  ...  C.J.T. acknowledges financial support by SBF ͑Switzerland͒ through research project C05.0148 ͑Physics of Risk͒.  ... 
doi:10.1063/1.2945903 pmid:19045499 fatcat:tbejvmrfq5hjzhnh2cfkh53v5y

Synchronization of spatially extended chaotic systems with asymmetric coupling

S. Boccaletti, C. Mendoza, J. Bragard
2005 Brazilian journal of physics  
Possible consequences of such asymmetry induced effects in biological and natural systems are discussed.  ...  properties of the highly coupled synchronized motion.  ...  Introduction The synchronization of coupled chaotic systems has been a topic of intense study since 1990 [1] .  ... 
doi:10.1590/s0103-97332005000300008 fatcat:nh4mexywhjgldn5mi5y4nijnie

Synchronization of Extended Chaotic Systems with Long-Range Interactions: An Analogy to Lévy-Flight Spreading of Epidemics

Claudio Juan Tessone, Massimo Cencini, Alessandro Torcini
2006 Physical Review Letters  
Spatially extended chaotic systems with power-law decaying interactions are considered.  ...  Two coupled replicas of such systems synchronize to a common spatio-temporal chaotic state above a certain coupling strength.  ...  The aim of this Letter is to study the synchronization transition of extended chaotic systems with long-range spatial coupling.  ... 
doi:10.1103/physrevlett.97.224101 pmid:17155806 fatcat:geojcd2pt5bbhooemfxnvekofa

Asymmetric Coupling Effects in the Synchronization of Spatially Extended Chaotic Systems

J. Bragard, S. Boccaletti, H. Mancini
2003 Physical Review Letters  
Novel features such as asymmetry enhanced complete synchronization, limits for the appearance of phase synchronized states, and selection of the final synchronized dynamics are reported and characterized  ...  We analyze the effects of asymmetric couplings in setting different synchronization states for a pair of unidimensional fields obeying complex Ginzburg-Landau equations.  ...  More recently, the interest moved to the study of synchronization phenomena in space-extended systems, such as large populations of coupled chaotic units and neural networks [4] , globally or locally  ... 
doi:10.1103/physrevlett.91.064103 pmid:12935079 fatcat:iiyutk7lvzcwpaartd6kltjgte

Synchronization of spatially extended chaotic systems in the presence of asymmetric coupling

J. Bragard, S. Boccaletti, C. Mendoza, H. G. E. Hentschel, H. Mancini
2004 Physical Review E  
Lett. 91, 064103 (2003)] we described the effects of asymmetric coupling configurations on the synchronization of spatially extended systems.  ...  We analyze the process of synchronization in the presence of asymmetries when the dynamics is affected by the presence of phase singularities, and show that defects tend to anchor one system to the other  ...  Recently, interest has moved to the study of synchronization phenomena in space-extended systems, such as large populations of coupled chaotic units and neural networks [8] , globally or locally coupled  ... 
doi:10.1103/physreve.70.036219 pmid:15524624 fatcat:byxmwltstvb5ri6tpiv666mdn4

ANOMALOUS SYNCHRONIZATION OF SPATIALLY EXTENDED CHAOTIC SYSTEMS IN THE PRESENCE OF ASYMMETRIC COUPLING

S. BOCCALETTI, C. MENDOZA, J. BRAGARD
2005 Fluctuation and Noise Letters  
Communicated by Werner Ebeling and Bernardo Spagnolo This paper describes the effects of an asymmetric coupling in the synchronization of two spatially extended systems.  ...  the synchronized dynamics, as well as in selecting the statistical and dynamical properties of the synchronized motion.  ...  is Anomalous synchronization of spatially extended chaotic systems enough to produce an excellent agreement between the SDE and the full CGLE models for the whole range of c.  ... 
doi:10.1142/s0219477505002628 fatcat:nj7tvbbwgnbmdjwhthqlqnlrui

Control and Synchronization of Chaotic and Hyperchaotic Lorenz Systems via Extended Backstepping Techniques

O. S. Onma, O. I. Olusola, A. N. Njah
2014 Journal of Nonlinear Dynamics  
We propose novel controllers for stabilization and tracking of chaotic and hyperchaotic Lorenz systems using extended backstepping techniques.  ...  Based on the proposed approach, generalized weighted controllers were designed to control chaotic behaviour as well as to achieve synchronization in chaotic and hyperchaotic Lorenz systems.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/861727 fatcat:jo3hilj2ubeglcm6t7lh63lvte

Adaptive sliding-mode control of chaotic permanent magnet synchronous motor system based on extended state observer

Chen Qiang, Nan Yu-Rong, Xing Ke-Xin
2014 Wuli xuebao  
An adaptive sliding-mode control scheme based on extended state observer (ESO) is proposed for permanent magnet synchronous motor (PMSM) chaotic system with some immesureable states.  ...  Simulation results show that the proposed controller can improve the chattering problem of the sliding-mode control and enhance the robustness of the system.  ...  韩京清 [26] 提出自抗扰控制技术, 通过设 计扩张状态观测器 (extended state observer, ESO) 观测系统的未知状态和不确定项, 将系统近似为一 个线性系统来处理. 该方法对系统模型敏感度较 低, 且对非线性扰动具有较强的鲁棒性, 因此在很 多领域得到了广泛应用 [27−30] .  ... 
doi:10.7498/aps.63.220506 fatcat:pyqvfiq6y5hu5ouahsvwf7muau

Generalized synchronization in coupled Ginzburg-Landau equations and mechanisms of its arising

Alexander E. Hramov, Alexey A. Koronovskii, Pavel V. Popov
2005 Physical Review E  
The mechanism resulting in the generalized synchronization regime arising in the coupled spatially extended chaotic systems demonstrating spatiotemporal chaotic oscillations has been described.  ...  The cause of the generalized synchronization occurrence is studied with the help of the modified Ginzburg-Landau equation with additional dissipation.  ...  However, the generalized synchronization of the spatially extended chaotic systems has not been studied in detail.  ... 
doi:10.1103/physreve.72.037201 pmid:16241618 fatcat:c2b7pikx5bdujexee3fffnym7m

Chaotic synchronization in coupled spatially extended beam–plasma systems

Roman A. Filatov, Alexander E. Hramov, Alexey A. Koronovskii
2006 Physics Letters A  
The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam-plasma Pierce systems.  ...  In case of unidirectional coupling the generalized synchronization regime has been observed in the spatially extended beam-plasma systems.  ...  Acknowledgements This work has been supported by CRDF (grant REC-006), the Supporting program of leading Russian scientific schools (project NSh-4167.2006.2) and Russian Foundation for Ba-  ... 
doi:10.1016/j.physleta.2006.05.039 fatcat:3aunlkebbbfszihmttfbjk7tu4

Globally exponential synchronization criterion of chaot-ic oscillators using active control

Israr Ahmad, Sharifa Al Mahrouqi, Mohammad Shahzad
2017 International Journal of Advanced Mathematical Sciences  
This research paper focuses the globally exponential synchronization between two identical and two nonidentical chaotic oscillators.  ...  A comparison, based upon the synchronization speed, cost and quality have been performed with our study of the previously published results.  ...  Description of the chaotic systems The extended Bonhoeffer van-der pol chaotic oscillator Electric circuits are one of the natural physical systems and it can be characterized by a variety of equations  ... 
doi:10.14419/ijams.v5i2.7770 fatcat:afouf3weonfpzlyddnxf4cwibe

Synchronization of Chaotic Systems via Active Disturbance Rejection Control

Fayiz Abu Khadra
2017 Intelligent Control and Automation  
This paper presents the use of active disturbance rejection control method (ADRC) to synchronize two different chaotic systems.  ...  The numerical results are presented for the synchronization between the Duffing-Holmes system and the van der pol system. The numerical results presented show the effectiveness of the proposed method.  ...  ADRC Synchronization of Two Chaotic Systems The synchronization of two chaotic systems is considered as a tracking control problem.  ... 
doi:10.4236/ica.2017.82007 fatcat:mtmuofcsa5auzb54io44virgf4

Synchronization and control of cellular automata [article]

Franco Bagnoli, Raul Rechtman
2009 arXiv   pre-print
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force".  ...  This is particularly true for extended systems that exhibit stable chaos, that is, systems which are not chaotic in the usual sense, but are unpredictable for finite perturbations.  ...  However, for chaotic systems, this state is unstable. Extended systems Natural systems, however, are rarely low-dimensional.  ... 
arXiv:0902.0231v1 fatcat:7iklhgg3tbgjxlaelgda2yomyy

Synchronization and Control of Cellular Automata [chapter]

Franco Bagnoli, Samira El Yacoubi, Raúl Rechtman
2010 Lecture Notes in Computer Science  
We study the problem of targeted synchronization of stable chaotic extended systems, i.e., systems which are not chaotic in the usual sense, but are unpredictable for finite perturbations.  ...  We show that the usual approach may lead to counter intuitive results, but that it is possible to exploit the characteristics of the system in order to reduce the distance between two replicas with less  ...  It is generally assumed that a system is chaotic if λ 0 > 0 and stable if λ 0 < 0. The largest Lyapunov exponent λ 0 (LLE) does not capture all the chaotic characteristics of an extended system.  ... 
doi:10.1007/978-3-642-15979-4_21 fatcat:hawjoxo4ojcs7gckihrozltr7i
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