1
|
Zhu S, Gan L. Incomplete phase-space method to reveal time delay from scalar time series. Phys Rev E 2016; 94:052210. [PMID: 27967148 DOI: 10.1103/physreve.94.052210] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2016] [Indexed: 11/07/2022]
Abstract
A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will show local clustering phenomenon after the component reordering procedure proposed in this work. We find that information captured by the incomplete two-dimensional reconstructed phase-space is related to the time delay τ_{0} present in the system, and will be transferred to the reordered component by the procedure of component reordering. We then propose the segmented mean variance (SMV) from the reordered component to identify the time delay τ_{0} of the system. The proposed SMV shows clear maximum when the embedding delay τ of the incomplete reconstruction matches the time delay τ_{0} of the chaotic system. Numerical data generated by a time-delay system based on the Mackey-Glass equation operating in the chaotic regime are used to illustrate the effectiveness of the proposed SMV. Experimental results show that the proposed SMV is robust to additive observational noise and is able to recover the time delay of the chaotic system even though the amount of data is relatively small and the feedback strength is weak. Moreover, the time complexity of the proposed method is quite low.
Collapse
Affiliation(s)
- Shengli Zhu
- Center for Cyber Security, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Lu Gan
- Center for Cyber Security, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| |
Collapse
|
2
|
Wu JG, Wu ZM, Xia GQ, Feng GY. Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system. OPTICS EXPRESS 2012; 20:1741-1753. [PMID: 22274517 DOI: 10.1364/oe.20.001741] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
In this paper, evolution of time delay (TD) signature of chaos generated in a mutual delay-coupled semiconductor lasers (MDC-SLs) system is investigated experimentally and theoretically. Two statistical methods, including self-correlation function (SF) and permutation entropy (PE), are used to estimate the TD signature of chaotic time series. Through extracting the characteristic peak from the SF curve, a series of TD signature evolution maps are firstly obtained in the parameter space of coupled strength and frequency detuning. Meantime, the influences of injection current on the evolution maps of TD signature have been discussed, and the optimum scope of TD signature suppression is also specified. An overall qualitative agreement between our theoretical and experimental results is obtained.
Collapse
Affiliation(s)
- Jia-Gui Wu
- School of Physics, Southwest University, Chongqing, China
| | | | | | | |
Collapse
|
3
|
|
4
|
Suresh R, Senthilkumar DV, Lakshmanan M, Kurths J. Global phase synchronization in an array of time-delay systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:016215. [PMID: 20866715 DOI: 10.1103/physreve.82.016215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2010] [Indexed: 05/29/2023]
Abstract
We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.
Collapse
Affiliation(s)
- R Suresh
- Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli, India.
| | | | | | | |
Collapse
|
5
|
Sun Y, Ruan J. Synchronization in coupled time-delayed systems with parameter mismatch and noise perturbation. CHAOS (WOODBURY, N.Y.) 2009; 19:043113. [PMID: 20059209 DOI: 10.1063/1.3262488] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
In this paper, a design of coupling and effective sufficient condition for stable complete synchronization and antisynchronization of a class of coupled time-delayed systems with parameter mismatch and noise perturbation are established. Based on the LaSalle-type invariance principle for stochastic differential equations, sufficient conditions guaranteeing complete synchronization and antisynchronization with constant time delay are developed. Also delay-dependent sufficient conditions for the case of time-varying delay are derived by using the Lyapunov approach for stochastic differential equations. Numerical examples fully support the analytical results.
Collapse
Affiliation(s)
- Yongzheng Sun
- School of Sciences, China University of Mining and Technology, Xuzhou 221008, People's Republic of China.
| | | |
Collapse
|
6
|
Ghosh D. Generalized projective synchronization in time-delayed systems: nonlinear observer approach. CHAOS (WOODBURY, N.Y.) 2009; 19:013102. [PMID: 19334966 DOI: 10.1063/1.3054711] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
In this paper, we consider the projective-anticipating, projective, and projective-lag synchronization in a unified coupled time-delay system via nonlinear observer design. A new sufficient condition for generalized projective synchronization is derived analytically with the help of Krasovskii-Lyapunov theory for constant and variable time-delay systems. The analytical treatment can give stable synchronization (anticipatory and lag) for a large class of time-delayed systems in which the response system's trajectory is forced to have an amplitude proportional to the drive system. The constant of proportionality is determined by the control law, not by the initial conditions. The proposed technique has been applied to synchronize Ikeda and prototype models by numerical simulation.
Collapse
Affiliation(s)
- Dibakar Ghosh
- Department of Mathematics, Dinabandhu Andrews College, Garia, Calcutta, India.
| |
Collapse
|
7
|
|
8
|
Senthilkumar DV, Lakshmanan M. Delay time modulation induced oscillating synchronization and intermittent anticipatory/lag and complete synchronizations in time-delay nonlinear dynamical systems. CHAOS (WOODBURY, N.Y.) 2007; 17:013112. [PMID: 17411248 DOI: 10.1063/1.2437651] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete, and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay systems having two different time-delays, that is feedback delay with a periodic delay time modulation and a constant coupling delay. Intermittent anticipatory, intermittent lag, and complete synchronizations are shown to exist in the same system with identical delay time modulations in both the delays. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay with suitable stability condition is discussed. The intermittent anticipatory and lag synchronizations are characterized by the minimum of the similarity functions and the intermittent behavior is characterized by a universal asymptotic -32 power law distribution. It is also shown that the delay time carved out of the trajectories of the time-delay system with periodic delay time modulation cannot be estimated using conventional methods, thereby reducing the possibility of decoding the message by phase space reconstruction.
Collapse
Affiliation(s)
- D V Senthilkumar
- Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli-620 024, India.
| | | |
Collapse
|
9
|
Pisarchik AN, Flores-Carmona NJ, Carpio-Valadez M. Encryption and decryption of images with chaotic map lattices. CHAOS (WOODBURY, N.Y.) 2006; 16:033118. [PMID: 17014223 DOI: 10.1063/1.2242052] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We propose a secure algorithm for direct encryption and decryption of digital images with chaotic map lattices. The basic idea is to convert, pixel by pixel, the image color to chaotic logistic maps one-way coupled by initial conditions. After small numbers of iterations and cycles, the image becomes indistinguishable due to inherent properties of chaotic systems. Since the maps are coupled, the image can be completely recovered by the decryption algorithm if map parameters, number of iterations, number of cycles, and the image size are exactly known.
Collapse
Affiliation(s)
- A N Pisarchik
- Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, 37150 Leon, Guanajuato, Mexico
| | | | | |
Collapse
|
10
|
Kye WH, Choi M, Kim CM, Park YJ. Encryption with synchronized time-delayed systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:045202. [PMID: 15903715 DOI: 10.1103/physreve.71.045202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2004] [Revised: 10/26/2004] [Indexed: 05/02/2023]
Abstract
We propose a new communication scheme that uses time-delayed chaotic systems with delay time modulation. In this method, the transmitter encodes a message as an additional modulation of the delay time and then the receiver decodes the message by tracking the delay time. We demonstrate our communication scheme in a system of coupled logistic maps. Also we discuss the error of the transferred message due to an external noise and present its correction method.
Collapse
Affiliation(s)
- Won-Ho Kye
- National Creative Research Initiative Center for Controlling Optical Chaos, Pai-Chai University, Daejeon 302-735, Korea
| | | | | | | |
Collapse
|
11
|
Li S, Alvarez G, Chen G, Mou X. Breaking a chaos-noise-based secure communication scheme. CHAOS (WOODBURY, N.Y.) 2005; 15:13703. [PMID: 15836271 DOI: 10.1063/1.1856711] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
This paper studies the security of a secure communication scheme based on two discrete-time intermittently chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) The key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process is insecure against known/chosen-plaintext attacks. The first two defects mean that the scheme is not secure enough against brute-force attacks, and the third one means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. Yet it remains to be clarified if intermittent chaos could be used for designing secure chaotic cryptosystems.
Collapse
Affiliation(s)
- Shujun Li
- Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, China.
| | | | | | | |
Collapse
|
12
|
Shahverdiev EM, Shore KA. Generalized synchronization in time-delayed systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016201. [PMID: 15697692 DOI: 10.1103/physreve.71.016201] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2004] [Revised: 08/03/2004] [Indexed: 05/24/2023]
Abstract
We investigate the generalized synchronization between two unidirectionally linearly and nonlinearly coupled chaotic nonidentical Ikeda models and find existence conditions of the generalized synchronization. Also we study the chaos synchronization between nonidentical Ikeda models with variable feedback-delay times and find the existence and sufficient stability conditions for the retarded synchronization manifold with the coupling-delay lag time. Generalization of the approach to the wide class of nonlinear chaotic systems is also presented.
Collapse
Affiliation(s)
- E M Shahverdiev
- Institute of Physics, 33, H. Javid Avenue, 370143-Baku, Azerbaijan.
| | | |
Collapse
|
13
|
Li X, Zhang H, Xue Y, Hu G. Enhancing chaoticity of spatiotemporal chaos. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016216. [PMID: 15697707 DOI: 10.1103/physreve.71.016216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2004] [Revised: 10/29/2004] [Indexed: 05/24/2023]
Abstract
In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed.
Collapse
Affiliation(s)
- Xiaowen Li
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | | | | | | |
Collapse
|
14
|
Senthilkumar DV, Lakshmanan M. Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016211. [PMID: 15697702 DOI: 10.1103/physreve.71.016211] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2004] [Indexed: 05/24/2023]
Abstract
The existence of anticipatory, complete, and lag synchronization in a single system having two different time delays, that is, feedback delay tau1 and coupling delay tau2, is identified. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay tau2 with a suitable stability condition is discussed. In particular, it is shown that the stability condition is independent of the delay times tau1 and tau2. Consequently, for a fixed set of parameters, all the three types of synchronizations can be realized. Further, the emergence of exact anticipatory, complete, or lag synchronization from the desynchronized state via approximate synchronization, when one of the system parameters (b2) is varied, is characterized by a minimum of the similarity function and the transition from on-off intermittency via periodic structure in the laminar phase distribution.
Collapse
Affiliation(s)
- D V Senthilkumar
- Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620 024, India.
| | | |
Collapse
|
15
|
Lü H, Wang S, Li X, Tang G, Kuang J, Ye W, Hu G. A new spatiotemporally chaotic cryptosystem and its security and performance analyses. CHAOS (WOODBURY, N.Y.) 2004; 14:617-629. [PMID: 15446972 DOI: 10.1063/1.1772731] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
A one-way-coupled chaotic map lattice is proposed for cryptography of self-synchronizing stream cipher. The system performs basic floating-point analytical computation on real numbers, incorporating auxiliarily with few simple algebraic operations on integer numbers. Parallel encryption (decryption) operations of multiple chaotic sites are conducted. It is observed that the system has high practical security, fast encryption (decryption) speed with software realization, and excellent reliability against strong channel noise, and its overall cryptographic properties are considerably better than both known chaotic cryptosystems and currently used conventional cryptosystems, including the advanced encryption standard.
Collapse
Affiliation(s)
- Huaping Lü
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | | | | | | | | | | | | |
Collapse
|
16
|
Ryu JW, Kye WH, Lee SY, Kim MW, Choi M, Rim S, Park YJ, Kim CM. Effects of time-delayed feedback on chaotic oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036220. [PMID: 15524625 DOI: 10.1103/physreve.70.036220] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2004] [Revised: 06/11/2004] [Indexed: 05/24/2023]
Abstract
We study the effects of time-delayed feedback on chaotic systems where the delay time is both fixed (static case) and varying (dynamic case) in time. For the static case, typical phase coherent and incoherent chaotic oscillators are investigated. Detailed phase diagrams are investigated in the parameter space of feedback gain ( K ) and delay time ( tau ). Linear stability analysis, by assuming the time-delayed perturbation, varies as e(lambdat) where lambda is the eigenvalue, gives the boundaries of the stability islands and critical feedback gains ( K(c) ) for both Rössler oscillators and Lorenz oscillators. We also found that the stability island are found when the delay time is about tau= (n+ 1 / 2 ) T , where n is an integer and T is the average period of the chaotic oscillator. It is shown that these analytical predictions agree well with the numerical results. For the dynamic case, we investigate Rössler oscillator with periodically modulated delay time. Stability regimes are found for parameter space of feedback gain and modulation frequency in which it was impossible to be stabilized for a fixed delay time. We also trace the detailed routes to the stability near the island boundaries for both cases by investigating bifurcation diagrams.
Collapse
Affiliation(s)
- Jung-Wan Ryu
- National Creative Research Initiative Center for Controlling Optical Chaos, Pai-Chai University, Daejeon 302-735, Korea
| | | | | | | | | | | | | | | |
Collapse
|
17
|
Zhan M, Wang X, Gong X, Wei GW, Lai CH. Complete synchronization and generalized synchronization of one-way coupled time-delay systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:036208. [PMID: 14524869 DOI: 10.1103/physreve.68.036208] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2003] [Indexed: 05/24/2023]
Abstract
The complete synchronization and generalized synchronization (GS) of one-way coupled time-delay systems are studied. We find that GS can be achieved by a single scalar signal, and its synchronization threshold for different delay times shows the parameter resonance effect, i.e., we can obtain stable synchronization at a smaller coupling if the delay time of the driven system is chosen such that it is in resonance with the driving system. Near chaos synchronization, the desynchronization dynamics displays periodic bursts with the period equal to the delay time of the driven system. These features can be easily applied to the recovery of time-delay systems.
Collapse
Affiliation(s)
- Meng Zhan
- Temasek Laboratories, National University of Singapore, Singapore 119260
| | | | | | | | | |
Collapse
|
18
|
Chen JY, Wong KW, Cheng LM, Shuai JW. A secure communication scheme based on the phase synchronization of chaotic systems. CHAOS (WOODBURY, N.Y.) 2003; 13:508-514. [PMID: 12777114 DOI: 10.1063/1.1564934] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Phase synchronization of chaotic systems with both weak and strong couplings has recently been investigated extensively. Similar to complete synchronization, this type of synchronization can also be applied in secure communications. We develop a digital secure communication scheme that utilizes the instantaneous phase as the signal transmitted from the drive to the response subsystems. Simulation results show that the scheme is difficult to be broken by some traditional attacks. Moreover, it operates with a weak positive conditional Lyapunov exponent in the response subsystem.
Collapse
Affiliation(s)
- J Y Chen
- Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong, China
| | | | | | | |
Collapse
|
19
|
Wang S, Kuang J, Li J, Luo Y, Lu H, Hu G. Chaos-based secure communications in a large community. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:065202. [PMID: 12513338 DOI: 10.1103/physreve.66.065202] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2002] [Indexed: 05/24/2023]
Abstract
One-way coupled map lattices are used for cryptography in secure communication, based on spatiotemporal chaos synchronization. The sensitivity of synchronization between the encryption and decryption systems can be adjusted by varying the system size. With a suitable parameter combination, the cryptosystem can reach optimal trade-off of security and performance, i.e., it shows high security (resistant against the public-structure and known-plaintext attacks) together with fast encryption (and decryption) speed. An experiment of duplex voice transmission through university network is realized, which confirms the above advantages of our approach.
Collapse
Affiliation(s)
- Shihong Wang
- Department of Physics, Beijing Normal University, China
| | | | | | | | | | | |
Collapse
|
20
|
Ponomarenko VI, Prokhorov MD. Extracting information masked by the chaotic signal of a time-delay system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:026215. [PMID: 12241275 DOI: 10.1103/physreve.66.026215] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2002] [Indexed: 05/23/2023]
Abstract
We further develop the method proposed by Bezruchko et al. [Phys. Rev. E 64, 056216 (2001)] for the estimation of the parameters of time-delay systems from time series. Using this method we demonstrate a possibility of message extraction for a communication system with nonlinear mixing of information signal and chaotic signal of the time-delay system. The message extraction procedure is illustrated using both numerical and experimental data and different kinds of information signals.
Collapse
Affiliation(s)
- V I Ponomarenko
- Saratov Department of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences, Zelyonaya Street 38, Saratov 410019, Russia
| | | |
Collapse
|
21
|
Wei GW, Zhao S. Synchronization and information processing by an on-off coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:056210. [PMID: 12059683 DOI: 10.1103/physreve.65.056210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2001] [Revised: 01/02/2002] [Indexed: 05/23/2023]
Abstract
This paper proposes an on-off coupling process for chaos synchronization and information processing. An in depth analysis for the net effect of a conventional coupling is performed. The stability of the process is studied. We show that the proposed controlled coupling process can locally minimize the smoothness and the fidelity of dynamical data. A digital filter expression for the on-off coupling process is derived and a connection is made to the Hanning filter. The utility and robustness of the proposed approach is demonstrated by chaos synchronization in Duffing oscillators, the spatiotemporal synchronization of noisy nonlinear oscillators, the estimation of the trend of a time series, and restoration of the contaminated solution of the nonlinear Schrödinger equation.
Collapse
Affiliation(s)
- G W Wei
- Department of Computational Science, National University of Singapore, Singapore 117543, Singapore
| | | |
Collapse
|
22
|
Bezruchko BP, Karavaev AS, Ponomarenko VI, Prokhorov MD. Reconstruction of time-delay systems from chaotic time series. PHYSICAL REVIEW E 2001; 64:056216. [PMID: 11736063 DOI: 10.1103/physreve.64.056216] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2001] [Revised: 06/18/2001] [Indexed: 11/07/2022]
Abstract
We propose a method that allows one to estimate the parameters of model scalar time-delay differential equations from time series. The method is based on a statistical analysis of time intervals between extrema in the time series. We verify our method by using it for the reconstruction of time-delay differential equations from their chaotic solutions and for modeling experimental systems with delay-induced dynamics from their chaotic time series.
Collapse
Affiliation(s)
- B P Bezruchko
- Saratov Department of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov, 410019, Russia
| | | | | | | |
Collapse
|
23
|
Udaltsov VS, Goedgebuer JP, Larger L, Rhodes WT. Communicating with optical hyperchaos: information encryption and decryption in delayed nonlinear feedback systems. PHYSICAL REVIEW LETTERS 2001; 86:1892-1895. [PMID: 11290275 DOI: 10.1103/physrevlett.86.1892] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2000] [Revised: 09/29/2000] [Indexed: 05/23/2023]
Abstract
Recent theoretical studies and experimental demonstrations have shown the possibility of using chaos for the encryption of message signals in communication systems. Chaos is generated by systems with delayed nonlinear feedback, which feature hyperchaotic (i.e., of high dimensionality) dynamics. The different ways for the injection of the information in the emitter and the process of the synchronization of the receiver are considered. The analysis of all the possibilities can be used to choose the correct topology of communication systems and, more generally, to explain the behavior of any chaotic systems ruled by nonlinear difference-differential equations.
Collapse
Affiliation(s)
- V S Udaltsov
- GTL-CNRS TELECOM, UMR CNRS 6603, Georgia Tech Lorraine, 57070 Metz, France
| | | | | | | |
Collapse
|
24
|
Yaowen L, Guangming G, Hong Z, Yinghai W, Liang G. Synchronization of hyperchaotic harmonics in time-delay systems and its application to secure communication. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:7898-7904. [PMID: 11138072 DOI: 10.1103/physreve.62.7898] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2000] [Revised: 07/31/2000] [Indexed: 05/23/2023]
Abstract
We present a predictor-feedback method for synchronizing chaotic systems in this paper. By using this method, two structurally equivalent or nonequivalent systems can be synchronized very effectively and quickly. Moreover, the feedback perturbation can be switched on even if trajectories of the two systems are far from each other. Therefore, this method is applicable to real-world experimental systems, especially to some fast experimental systems. The validity of this method is demonstrated by synchronizing hyperchaotic harmonics in a time-delay system. As an application, we introduce how messages can be encoded, transmitted, and decoded using this technique. We suggest taking use of the multistability of time-delay systems to improve the performance of the secure communication.
Collapse
Affiliation(s)
- L Yaowen
- Department of Physics, Lanzhou University, Lanzhou 730000, China
| | | | | | | | | |
Collapse
|